BIMSA > 尼古拉·莱舍提金
教授 尼古拉·莱舍提金

单位: 清华丘成桐数学科学中心, 北京雁栖湖应用数学研究院

团队: 数学物理

办公室: A3-2-307

邮箱: nreshetikhin@bimsa.cn

研究方向: 量子场论、表示论、低维拓扑

个人主页: https://ymsc.tsinghua.edu.cn/en/info/1031/1880.htm

个人简介

Nicolai Reshetikhin教授出生于前苏联列宁格勒，即现俄罗斯圣彼得堡。1982年，毕业于列宁格勒国立大学，获得学士学位与硕士学位。1984年，毕业于斯捷克洛夫数学研究所，获得博士学位。曾在哈佛大学、加州大学伯克利分校、阿姆斯特丹大学等知名大学任教。两次受邀在ICM国际数学家大会做报告，其中一次为大会报告。Reshetikhin教授的主要研究方向为量子拓扑，量子群及其表示，经典与量子可积系统，可积统计力学模型。他是量子群理论创始人之一、Reshetikhin-Turaev不变量的作者之一，在量子可积系统理论、泊松几何、辛几何、Quantum Kac-Moody代数有重要研究成果。2010年当选为皇家丹麦研究院外籍院士，2021年当选为美国数学会会士。

研究兴趣

  • Representation theory, Quantum field theory, Integrable systems

教育经历

  • 1982 - 1984      斯捷克洛夫数学研究所      博士
  • 1979 - 1982      列宁格勒大学      硕士,学士
  • 1975 - 1979      列宁格勒理工学院      学士

工作经历

  • 2022 -      北京雁栖湖应用数学研究院
  • 2021 -      清华大学      教授
  • 1997 - 2021      加州大学伯克利分校      教授
  • 1991 - 1997      加州大学伯克利分校      副教授
  • 1989 - 1991      哈佛大学      助理教授
  • 1984 - 1989      俄罗斯斯特克洛夫数学研究所      研究员

荣誉与奖项

  • 2022      Weyl-Wigner Award
  • 2010      "The Mathematics of Quantum Field Theory" plenary talk at the ICM-2010      Hyderabad, India, August 2010
  • 1990      45-minute talk, ICM1990, Kyoto Japan

出版物

  • [1] Andrii Liashyk, Nicolai Reshetikhin, Ivan Sechin, Quantum integrable systems on a classical integrable background, arXiv preprint arXiv:2405.17865 (2024)
  • [2] E Koelink, S Kolb, N Reshetikhin, B Vlaar, Hypergeometry, Integrability and Lie Theory, American Mathematical Society (2022)
  • [3] Nicolai Reshetikhin, Gus Schrader, Superintegrability of generalized Toda models on symmetric spaces, International Mathematics Research Notices, 2021(17), 12993-13010 (2021)
  • [4] S. Arthamonov, N. Reshetikhin, Superintegrable systems on moduli spaces of flat connections, Communications in Mathematical Physics, 386, 1337-1381 (2021)
  • [5] Christian Blanchet, Nathan Geer, Bertrand Patureau-Mirand, Nicolai Reshetikhin, Holonomy braidings, biquandles and quantum invariants of links with SL2(C) flat connections, Selecta Math., 26(2) (2020)
  • [6] Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin, A cellular topolog- ical field theory, Communications in Mathematical Physics, 374(2), 1229-1320 (2020)
  • [7] Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin, Poisson sigma model and semiclassical quantization of integrable systems, Reviews in Mathematical Physics, 30(06), 1840004 (2018)
  • [8] Nicolai Reshetikhin, Semiclassical geometry of integrable systems, Journal of Physics A: Mathematical and Theoretical, 51(16), 164001 (2018)
  • [9] N Reshetikhin, J Stokman, B Vlaar, Integral solutions to boundary quantum Knizhnik–Zamolodchikov equations, Advances in Mathematics, 323, 486-528 (2018)
  • [10] Alberto S. Cattaneo, Pavel Mnev, Nicolai Reshetikhin, Perturbative quan- tum gauge theories on manifolds with boundary, Communications in Math-ematical Physics, 357(2), 631730 (2018)
  • [11] Nicolai Reshetikhin, Jasper Stokman, Bart Vlaar, Integral solutions to bound- ary quantum Knizhnik-Zamolodchikov equations, Advances in Mathematics, 323(7 January 2018), 486-528 (2018)
  • [12] D. Keating, N. Reshetikhin, A. Sridhar, Conformal limit for Dimer models on the hexagonal lattice, Записки научных семинаров ПОМИ, 473(0), 174-193 (2018)
  • [13] Nicolai Reshetikhin, Ananth Sridhar, Integrability of limit shapes of the six vertex model, Communications in Mathematical Physics, 356, 535-565 (2017)
  • [14] Nicolai Reshetikhin, Degenerate integrability of quantum spin Calogero-Moser systems, Lett.Math.Phys., 107(1), 187-200 (2017)
  • [15] Nicolai Reshetikhin, Degenerately integrable systems, Journal of Mathematical Sciences, 213, 769-785 (2016)
  • [16] Reshetikhin N.Y., Stokman J.V., Vlaar B., Boundary Quantum Knizhnik- Zamolodchikov Equations and Fusion, Annales Henri Poincar January 2016, 17(1), 137177 (2016)
  • [17] Nicolai Reshetikhin, Jasper Stokman and Bart Vlaar, Boundary quantum Knizhnik–Zamolodchikov equations and fusion, Annales Henri Poincaré, 17(1), 137-177 (2016)
  • [18] Nicolai, Reshetikhin, Jasper, Stokman, Bart, Vlaar, Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors, Communications in Mathematical Physics, 336, 953-986 (2015)
  • [19] Nicolai Reshetikhin, Boris Vertman, Combinatorial Quantum Field The- ory and Gluing Formula for Determinants, Lett. Math. Phys., 105(3), 309340 (2015)
  • [20] Nicolai Reshetikhin, Jasper Stokman and Bart Vlaar, Boundary Quantum Knizhnik–Zamolodchikov Equations and Bethe Vectors, Commun. Math. Phys., 336, 953-986 (2015)
  • [21] A Gerasimov, S Kharchev, D Lebedev, S Oblezin, Contemporary Mathematics Volume 391, 2005, Noncommutative Geometry and Representation Theory in Mathematical Physics: Satellite Conference to the Fourth European Congress of Mathematics, July 5-10, 2004, Karlstad University, Karlstad, Sweden, 391, 101 (2005)
  • [22] A.Kirillov, N.Yu.Reshetikhin, The Bethe ansatz and the combinatorics of Young tableaux, Zap. Nauch. Sem. LOMI, 155(1986), 65-115 (1987)
  • [23] A.Kirillov, N.Yu.Reshetikhin, The Yangians, Bethe ansatz and combinatorics, letters in mathematical physics, 12, 199-208 (1986)
  • [24] S Gukov, B Haghighat, N Reshetikhin, Foams and KZ-equations in Rozansky-Witten theories, Nuclear Physics B, 116856 (2025)
  • [25] P Mnev, Lecture notes on conformal field theory, arXiv preprint arXiv:2501.06616 (2025)
  • [26] H De Clercq, N Reshetikhin, J Stokman, Graphical calculus for quantum vertex operators, I: The dynamical fusion operator, Communications in Mathematical Physics, 405(6) (2024)
  • [27] S Gukov, B Haghighat, Y Liu, N Reshetikhin, Irregular KZ equations and Kac-Moody representations, arXiv preprint arXiv:2412.16929 (2024)
  • [28] H De Clercq, N Reshetikhin, J Stokman, Graphical calculus for quantum vertex operators, II: q-KZB and coordinate Macdonald-Ruijsenaars equations, arXiv preprint arXiv:2411.17306 (2024)
  • [29] JV Stokman, N Reshetikhin, Correction to: -point spherical functions and asymptotic boundary KZB equations, Inventiones mathematicae, 237(2), 869-870 (2024)
  • [30] A Lachowska, O Postnova, N Reshetikhin, D Solovyev, Tensor powers of vector representation of at even roots of unity, Other (2024)
  • [31] F Colomo, J de Gier, P Di Francesco, N Reshetikhin, D Serban, H Spohn, Randomness, Integrability and Universality (2024)
  • [32] N Reshetikhin, Spin Calogero-Moser periodic chains and two dimensional Yang-Mills theory with corners, arXiv preprint arXiv:2303.10579 (2023)
  • [33] N Reshetikhin, Periodic and open classical spin Calogero-Moser chains, arXiv preprint arXiv:2302.14281 (2023)
  • [34] N Reshetikhin, J Stokman, Quantum superintegrable spin systems on graph connections, arXiv preprint arXiv:2305.02767 (2023)
  • [35] N Reshetikhin, The acceptance speech of the 2022 Weyl-Wigner award, SciPost Physics Proceedings (2023)
  • [36] B Haghighat, Y Liu, N Reshetikhin, Flat Connections from Irregular Conformal Blocks, arXiv preprint arXiv:2311.07960 (2023)
  • [37] OV Postnova, NY Reshetikhin, On the Asymptotics of Multiplicities for Large Tensor Product of Representations of Simple Lie Algebras., Journal of Mathematical Sciences, 275(3) (2023)
  • [38] JV Stokman, N Reshetikhin, N-point spherical functions and asymptotic boundary KZB equations, Inventiones mathematicae, 229(1), 1-86 (2022)
  • [39] E Frenkel, D Hernandez, N Reshetikhin, Folded quantum integrable models and deformed W-algebras, Letters in Mathematical Physics, 112(4) (2022)
  • [40] P Belov, N Reshetikhin, The two-point correlation function in the six-vertex model, Journal of Physics A: Mathematical and Theoretical, 55(15) (2022)
  • [41] D Keating, N Reshetikhin, A Sridhar, Integrability of limit shapes of the inhomogeneous six vertex model, Communications in Mathematical Physics, 391(3), 1181-1207 (2022)
  • [42] OV Postnova, NY Reshetikhin, On the asymptotics of multiplicities for large tensor product of representations of simple Lie algebras, Записки научных семинаров ПОМИ(509), 185-200 (2021)
  • [43] E Frenkel, D Hernandez, N Reshetikhin, arXiv: Folded quantum integrable models and deformed W-algebras (2021)
  • [44] AS Cattaneo, P Mnev, N Reshetikhin, A cellular topological field theory, Communications in Mathematical Physics, 374, 1229-1320 (2020)
  • [45] C Blanchet, N Geer, B Patureau-Mirand, N Reshetikhin, Holonomy braidings, biquandles and quantum invariants of links with$SL2(C)$flat connections, Selecta Mathematica, 26(2) (2020)
  • [46] O Postnova, N Reshetikhin, On multiplicities of irreducibles in large tensor product of representations of simple Lie algebras, Letters in Mathematical Physics, 110(1), 147-178 (2020)
  • [47] N Reshetikhin, J Stokman, Asymptotic boundary KZB operators and quantum Calogero-Moser spin chains, arXiv preprint arXiv:2012.13497 (2020)
  • [48] D Dumbaugh, P Daskalopoulos, A Vershik, L Kapitanski, N Reshetikhin et al., The ties that bind Olga Alexandrovna Ladyzhenskaya and the 2022 ICM in St. Petersburg, Notices of the American Mathematical Society, 67(3) (2020)
  • [49] N Reshetikhin, Spin Calogero-Moser models on symmetric spaces, arXiv preprint arXiv:1903.03685 (2019)
  • [50] D Keating, N Reshetikhin, A Sridhar, Conformal Limit for Dimer Models on the Hexagonal Lattice., Journal of Mathematical Sciences, 242(5) (2019)
  • [51] AS Cattaneo, P Mnev, N Reshetikhin, Perturbative quantum gauge theories on manifolds with boundary, Communications in Mathematical Physics, 357, 631-730 (2018)
  • [52] N Reshetikhin, A Sridhar, Limit shapes of the stochastic six vertex model, Communications in Mathematical Physics, 363, 741-765 (2018)
  • [53] N Kitanine, RI Nepomechie, N Reshetikhin, Quantum integrability and quantum groups: a special issue in memory of Petr P Kulish, Journal of Physics A: Mathematical and Theoretical, 51(11) (2018)
  • [54] A Its, N Reshetikhin, Preface: Introduction to special issue: In memory of Ludwig Faddeev, Journal of Mathematical Physics, 59(9) (2018)
  • [55] N RESHETIKHIN, GUS SCHRADER, SUPERINTEGRABILITY OF SYMMETRIC TODA, arXiv preprint arXiv:1802.00356 (2018)
  • [56] N Reshetikhin, Degenerate integrability of quantum spin Calogero–Moser systems, Letters in Mathematical Physics, 107, 187-200 (2017)
  • [57] IY Aref'eva, VE Zakharov, VV Kozlov, IM Krichever, VP Maslov et al., Ludwig Dmitrievich Faddeev, Russian Mathematical Surveys, 72(6) (2017)
  • [58] N Reshetikhin, M Semenov-Tian-Shansky, L Takhtajan, LD Faddeev:(March 23, 1934-February 26, 2017), International Association of Mathematical Physics (IAMP) News Bulletin (2017)
  • [59] AS Cattaneo, P Mnev, N Reshetikhin, Perturbative BV theories with Segal-like gluing, arXiv preprint arXiv:1602.00741 (2016)
  • [60] F Colomo, P Fendley, A Pronko, N Reshetikhin, P Wiegmann et al., Statistical Mechanics, Integrability and Combinatorics, Il Colle di Galileo, 5(1), 77-81 (2016)
  • [61] R Borcherds, M Haiman, N Reshetikhin, V Serganova, T Johnson-Freyd, Part I: Lie Groups (2016)
  • [62] B Booss-Bavnbek, M Lesch, G Marinescu, N Reshetikhin, B Vertman, Interfaces between Geometric Analysis and Mathematical Physics: July 2016, Scientific report (2016)
  • [63] L FADDEEV, N RESHETIKHIN, L TAKHTAJAN, Leningrad Branch of VA Steklov Mathematical Institute of the Academy of, Fifty Years of Mathematical Physics: Selected Works of Ludwig Faddeev, 2 (2016)
  • [64] N Reshetikhin, B Vertman, Combinatorial quantum field theory and gluing formula for determinants, Letters in Mathematical Physics, 105, 309-340 (2015)
  • [65] AS Cattaneo, P Mnev, N Reshetikhin, Semiclassical quantization of classical field theories, Mathematical Aspects of Quantum Field Theories, 275-324 (2015)
  • [66] M Aganagic, I Agol, D Auroux, G Bergman, R Bryant, A Chorin, M Christ et al., Sincerely, University of California, Berkeley (2015)
  • [67] AS Cattaneo, P Mnev, N Reshetikhin, Classical BV theories on manifolds with boundary, Communications in Mathematical Physics, 332, 535-603 (2014)
  • [68] Q Chen, N Reshetikhin, Recursion formulas for HOMFLY and Kauffman invariants, Journal of Knot Theory and Its Ramifications, 23(5) (2014)
  • [69] N Reshetikhin, J Stokman, B Vlaar, Reflection quantum Knizhnik-Zamolodchikov equations and Bethe vectors, arXiv preprint arXiv:1305.1113 (2013)
  • [70] C De Concini, D Hernandez, N Reshetikhin, Geometry of the analytic loop group, Advances in Mathematics, 238, 290-321 (2013)
  • [71] AS Cattaneo, P Mnev, N Reshetikhin, Classical and quantum Lagrangian field theories with boundary, arXiv preprint arXiv:1207.0239 (2012)
  • [72] C Boutillier, S Mkrtchyan, N Reshetikhin, P Tingley, Random skew plane partitions with a piecewise periodic back wall, Annales Henri Poincaré, 13, 271-296 (2012)
  • [73] P Di Francesco, N Reshetikhin, Asymptotic shapes with free boundaries, Communications in Mathematical Physics, 309, 87-121 (2012)
  • [74] AS Cattaneo, P Mnëv, N Reshetikhin, Classical BV theories on manifolds with boundaries, arXiv preprint math-ph/1201.0290 (2012)
  • [75] N Reshetikhin, C Stroppel, B Webster, Schur–Weyl-Type Duality for Quantized(1|1), the Burau Representation of Braid Groups, and Invariants of Tangled Graphs, Perspectives in Analysis, Geometry, and Topology (2012)
  • [76] N Reshetikhin, Quantum Deformations of SL/B and its Schubert Varieties n, ICM-90 Satellite Conference Proceedings: Special Functions (2012)
  • [77] R Borcherds, M Haiman, N Reshetikhin, V Serganova, Berkeley Lectures on Lie Groups and Quantum Groups, ed. Anton Geraschenko and Theo Johnson-Freyd (2011)
  • [78] K Hasegawa, T Hayashi, S Hosono, Y Yamada, Program of the Conference, Exploring New Structures and Natural Constructions in Mathematical Physics 61 (2011)
  • [79] N Reshetikhin, Lectures on the integrability of the six-vertex model, Exact methods in low-dimensional statistical physics and quantum computing … (2010)
  • [80] N Reshetikhin, Lectures on quantization of gauge systems, New Paths Towards Quantum Gravity, 125-190 (2010)
  • [81] R Kashaev, N Reshetikhin, Invariants of tangles with flat connections in their complements, arXiv preprint arXiv:1008.1384 (2010)
  • [82] K Palamarchuk, N Reshetikhin, The 6-vertex model with fixed boundary conditions, arXiv preprint arXiv:1010.5011 (2010)
  • [83] I Affleck, F Alet, JL Cardy, NR Cooper, B Duplantier, MV Feigel'man et al., Exact Methods in Low-dimensional Statistical Physics and Quantum Computing: École D'été de Physique Des Houches, Session LXXXIX, 30 June-1 August 2008, École Thématique Du CNRS, Oxford University Press (2010)
  • [84] T JOLICOEUR, R KENYON, A KITAEV, I KOSTOV, W KRAUTH et al., STUDENTS AND AUDITORS, Exact Methods in Low-dimensional Statistical Physics and Quantum Computing … (2010)
  • [85] N Geer, N Reshetikhin, On Invariants of Graphs Related to Quantum at Roots of Unity, Letters in Mathematical Physics, 88(1), 321-331 (2009)
  • [86] D Orlando, S Reffert, N Reshetikhin, On domain wall boundary conditions for the XXZ spin Hamiltonian, arXiv preprint arXiv:0912.0348 (2009)
  • [87] VK Murty, SELECTED MATHEMATICAL REVIEWS, AMERICAN MATHEMATICAL SOCIETY, 46(3), 485-487 (2009)
  • [88] D Cimasoni, N Reshetikhin, Dimers on surface graphs and spin structures. II, Communications in mathematical physics, 281, 445-468 (2008)
  • [89] N Reshetikhin, Topological quantum field theory: 20 years later, European Congress of Mathematics, 333-377 (2008)
  • [90] A Okounkov, N Reshetikhin, Random skew plane partitions and the Pearcey process, Communications in Mathematical Physics, 269, 571-609 (2007)
  • [91] D Cimasoni, N Reshetikhin, Dimers on surface graphs and spin structures. I, Communications in Mathematical Physics, 275, 187-208 (2007)
  • [92] RM Kashaev, N Reshetikhin, Symmetrically factorizable groups and set-theoretical solutions of the pentagon equation, Contemporary Mathematics, 433, 267-280 (2007)
  • [93] N Reshetikhin, The Mathematical Work of the 2006 Fields Medalists, Notices of the AMS, 54(3) (2007)
  • [94] N Reshetikhin, The work of Andrei Okounkov, Notices of the American Mathematical Society, 54(3), 388-390 (2007)
  • [95] A Okounkov, N Reshetikhin, C Vafa, Quantum Calabi-Yau and classical crystals, The unity of Mathematics: In Honor of the Ninetieth Birthday of IM Gelfand … (2006)
  • [96] AY Okounkov, NY Reshetikhin, The birth of a random matrix, Moscow Mathematical Journal, 6(3), 553-566 (2006)
  • [97] A Okounkov, N Reshetikhin, C Vafa, The unity of mathematics, Progress in Mathematics, 244, 597-618 (2006)
  • [98] N Reshetikhin, Some algebraic and analytic structures in integrable systems, Low-Dimensional Models in Statistical Physics and Quantum Field Theory (2006)
  • [99] N Reshetikhin, K Palamarchuk, PoS (Solvay) 012 The 6-vertex model with fixed boundary conditions. (2006)
  • [100] D Allison, N Reshetikhin, Numerical stu\-dy of the 6-vertex model with domain wall boundary conditions, Annales de l'institut Fourier, 55(6), 1847-1869 (2005)
  • [101] C De Concini, C Procesi, N Reshetikhin, M Rosso, Hopf algebras with trace and representations, Inventiones mathematicae, 161, 1-44 (2005)
  • [102] N Reshetikhin, A Veselov, Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps, arXiv preprint math/0512328 (2005)
  • [103] R Kashaev, N Reshetikhin, Braiding for the quantum gl_2 at roots of unity, arXiv preprint math/0410182 (2004)
  • [104] AS Cattaneo, P Mnëv, N Reshetikhin, Perturbative BV-BFV theories on manifolds with boundary, preparation (2004)
  • [105] A Okounkov, N Reshetikhin, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, Journal of the American Mathematical Society, 16(3), 581-603 (2003)
  • [106] N Reshetikhin, Degenerate integrability of the spin Calogero–Moser systems and the duality with the spin Ruijsenaars systems, Letters in Mathematical Physics, 63, 55-71 (2003)
  • [107] N Reshetikhin, Integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structure, Communications in mathematical physics, 242, 1-29 (2003)
  • [108] N RESHETIKHIN, M ROSSO, Hopf algebras with trace and representations DE CONCINI, Corrado PROCESI, Claudio (2003)
  • [109] R Kashaev, N Reshetikhin, Invariants of tangles with flat connections in their complements. I. Invariants and holonomy R-matrices, arXiv preprint math/0202211 (2002)
  • [110] R Kashaev, N Reshetikhin, Invariants of links with flat connections in their complements. II. Holonomy R-matrices related to quantized universal enveloping algebras at roots of 1, arXiv preprint math/0202212 (2002)
  • [111] E Frenkel, N Reshetikhin, Quantum affine algebras and deformations of the Virasoro and, arXiv preprint q-alg/9505025 (2002)
  • [112] N Reshetikhin, M Yakimov, Quantum invariant measures, Communications in Mathematical Physics, 224, 399-426 (2001)
  • [113] T Hoffmann, J Kellendonk, N Kutz, N Reshetikhin, Factorization Dynamics and Coxeter--Toda Lattices, Communications in Mathematical Physics, 212, 297-321 (2000)
  • [114] N Reshetikhin, M Yakimov, Deformation quantization of Lagrangian fiber bundles, Conférence Moshé Flato (2000)
  • [115] N Reshetikhin, Characteristic systems on Poisson Lie groups and their quantization, CRM Proc (2000)
  • [116] N Reshetikhin, L Takhtajan, Deformation quantization of Kahler manifolds, arXiv preprint math/9907171 (1999)
  • [117] E Frenkel, N Reshetikhin, Contemporary Mathematics Volume 248, 1999, Recent Developments in Quantum Affine Algebras and Related Topics (1999)
  • [118] E Frenkel, N Reshetikhin, The q-characters of representations of quantum affine algebras and deformations of W-algebras, arXiv preprint math/9810055 (1998)
  • [119] E Frenkel, N Reshetikhin, MA Semenov-Tian-Shansky, Drinfeld–sokolov reduction for difference operators and deformations of-algebras¶ i. the case of virasoro algebra, Communications in mathematical physics, 192(3), 605-629 (1998)
  • [120] JE Andersen, J Mattes, N Reshetikhin, Quantization of the algebra of chord diagrams, Mathematical Proceedings of the Cambridge Philosophical Society, 124(3), 451-467 (1998)
  • [121] PJ Sally Jr, M Flato, J Lepowsky, N Reshetikhin, GJ Zuckerman, Mathematical aspects of conformal and topological field theories and quantum groups, 1994, Contemporary Mathematics, 217, 175-175 (1998)
  • [122] E Frenkel, N Reshetikhin, Deformations of W-algebras associated to simple Lie algebras, arXiv preprint q-alg/9708006 (1997)
  • [123] E Frenkel, N Reshetikhin, Towards deformed chiral algebras, arXiv preprint q-alg/9706023 (1997)
  • [124] RM Kashaev, N Reshetikhin, Affine Toda field theory as a 3-dimensional integrable system, Communications in Mathematical Physics, 188, 251-266 (1997)
  • [125] N Reshetikhin, J Mattes, From Infinite Dimensional Lie Algebras to Invariants of Knots, American Mathematical Society (1997)
  • [126] E Frenkel, N Reshetikhin, Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1, Communications in mathematical physics, 178(1), 237-264 (1996)
  • [127] JE Andersen, J Mattes, N Reshetikhin, The Poisson structure on the moduli space of flat connections and chord diagrams, Topology, 35(4), 1069-1083 (1996)
  • [128] V Bazhanov, A Bobenko, N Reshetikhin, Quantum discrete sine-Gordon model at roots of 1: integrable quantum system on the integrable classical background, Communications in Mathematical Physics, 175, 377-400 (1996)
  • [129] N Reshetikhin, AA Voronov, A Weinstein, Semiquantum geometry, arXiv preprint q-alg/9606007 (1996)
  • [130] AN Kirillov, NY Reshetikhin, Formulas for multiplicities of occurence of irreducible components in the tensor product of representations of simple Lie algebras, Journal of Mathematical Sciences, 80, 1768-1772 (1996)
  • [131] N Reshetikhin, Integrable discrete systems, Quantum Groups and their Applications in Physics, 445-487 (1996)
  • [132] M Polyak, N Reshetikhin, On 2D Yang-Mills theory and invariants of links, Deformation Theory and Symplectic Geometry, 223-246 (1996)
  • [133] N Reshetikhin, Quasitriangularity of quantum groups at roots of 1, Communications in mathematical physics, 170(1), 79-99 (1995)
  • [134] VV Bazhanov, NY Reshetikhin, Remarks on the quantum dilogarithm, Journal of Physics A: Mathematical and General, 28(8) (1995)
  • [135] VV Bazhanov, NY Reshetikhin, Chiral Potts model and the discrete Sine-Gordon model at roots of unity, Preprint arXiv: hep-th/0809.2351 (1995)
  • [136] B Feigin, E Frenkel, N Reshetikhin, Gaudin model, Bethe ansatz and critical level, Communications in Mathematical Physics, 166, 27-62 (1994)
  • [137] N Reshetikhin, A Varchenko, Quasiclassical asymptotics of solutions to the KZ equations, arXiv preprint hep-th/9402126 (1994)
  • [138] V Ginzburg, QUANTUM GROUPS AND FLAG VARIETIES. VICTOR GINZBURG, NICOLAI RESHETIKHIN ERIC VASSEROT, Mathematical aspects of conformal and topological field theories and quantum … (1994)
  • [139] NY Reshetikhin, H Saleur, Lattice regularization of massive and massless integrable field theories, Nuclear Physics B, 419(3), 507-528 (1994)
  • [140] P Sally, M Flato, J Lepowsky, N Reshetikhin, G Zuckerman, Mathematical aspects of conformal and topological field theories and quantum groups, American Mathematical Society (1994)
  • [141] J Mattes, N Reshetikhin, On invariants of tangles derived from balanced categories, Conference on Quantum Topology, 269-299 (1994)
  • [142] N Reshetikhin, Integrable systems with discrete time, Lectures given at “Enrico Fermi” international school of physics, Varenna (1994)
  • [143] J Mattes, M Polyak, N Reshetikhin, On invariants of 3-manifolds derived from abelian groups, Quantum topology, 324-338 (1993)
  • [144] AN Kirillov, NY Reshetikhin, Formulas for multiplicities of occurrence of irreducible components into the tensor product of representations of simple Lie algebras, Zapiski Nauchnykh Seminarov POMI, 205, 30-37 (1993)
  • [145] IB Frenkel, NY Reshetikhin, Quantum affine algebras and holonomic difference equations, Communications in Mathematical Physics, 146(1), 1-60 (1992)
  • [146] N Reshetikhin, The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem, Letters in Mathematical Physics, 26, 167-177 (1992)
  • [147] N Reshetikhin, Jackson-type integrals, Bethe vectors, and solutions to a difference analog of the Knizhnik-Zamolodchikov system, Letters in Mathematical Physics, 26(3), 153-165 (1992)
  • [148] V Lakshmibai, N Reshetikhin, Quantum flag and Schubert schemes, Contemp. Math, 134, 145-181 (1992)
  • [149] N Reshetikhin, Quantization of Lie bialgebras, International Mathematics Research Notices, 1992(7), 143-151 (1992)
  • [150] N Reshetikhin, Quantum supergroups, Quantum field theory, statistical mechanics, quantum groups and topology … (1992)
  • [151] IB Frenkel, NY Reshetikhin, Quantum affine algebras, commutative systems of difference equations and elliptic solutions to the Yang-Baxter equations, XXth International Conference on Differential Geometric (1992)
  • [152] M Herman, PJL Lebowitz, NY Reshetikhin, YG Sinai, MT Spencer et al., Chief Editor A. Jaffe, Cambridge, MA Editorial Board (1992)
  • [153] N Reshetikhin, VG Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Inventiones mathematicae, 103(1), 547-597 (1991)
  • [154] N Reshetikhin, S-matrices in integrable models of isotropic magnetic chains. I, Journal of Physics A: Mathematical and General, 24(14) (1991)
  • [155] NY Reshetikhin, A new exactly solvable case of an O (n)-model on a hexagonal lattice, Journal of Physics A: Mathematical and General, 24(10) (1991)
  • [156] NY Reshetikhin, Algebraic Bethe ansatz for SO (N)-invariant transfer matrices, Journal of Soviet Mathematics, 54, 940-951 (1991)
  • [157] V Lakshmibai, N Reshetikhin, Quantum Deformations of SL/B and its Schubert Varieties, ICM-90 Satellite Conference Proceedings: Special Functions, 149-168 (1991)
  • [158] N Reshetikhin, Invariants of links and 3-manifolds related to quantum groups, Int. Congr. Math., 2, 1373-1375 (1991)
  • [159] N Reshetikhin, Boston, MA 02115, Special Functions: Proceedings of the Hayashibara Forum (1991)
  • [160] M Aizenman, M Herman, PJL Lebowitz, NY Reshetikhin, R Schrieffer, Chief Editor A. Jaffef Cambridge, MA (1991)
  • [161] NY Reshetikhin, VG Turaev, Ribbon graphs and their invaraints derived from quantum groups, Communications in Mathematical Physics, 127, 1-26 (1990)
  • [162] N Reshetikhin, Multiparameter quantum groups and twisted quasitriangular Hopf algebras, Letters in Mathematical Physics, 20, 331-335 (1990)
  • [163] NY Reshetikhin, MA Semenov-Tian-Shansky, Central extensions of quantum current groups, Letters in Mathematical Physics, 19, 133-142 (1990)
  • [164] AN Kirillov, N Reshetikhin, $q$-Weyl group and a multiplicative formula for universal$R$-matrices (1990)
  • [165] N Reshetikhin, F Smirnov, Hidden quantum group symmetry and integrable perturbations of conformal field theories, Communications in Mathematical Physics, 131(1), 157-177 (1990)
  • [166] VV Bazhanov, N Reshetikhin, Restricted solid-on-solid models connected with simply laced algebras and conformal field theory, Journal of Physics A: Mathematical and General, 23(9) (1990)
  • [167] AN Kirillov, NY Reshetikhin, Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras, Journal of Soviet Mathematics, 52, 3156-3164 (1990)
  • [168] VV Bazhanov, NY Reshetikhin, Scattering amplitudes in offcritical models and RSOS integrable models, Progress of Theoretical Physics Supplement, 102, 301-318 (1990)
  • [169] V Lakshimibai, NY Reshetikhin, Quantum deformations of flag and Schubert schemes (1990)
  • [170] LD Faddeev, NY Reshetikhin, LA Takhtajan, Algebra i Analiz, 1 No. 1 (1989) 178, English transl: Leningr. Math. J 1, 193 (1990)
  • [171] A Babelon, N Reshetikhin, S Shatashvili, F Smirnoff, L Takhtajan, From Integrable Models to Quantum Groups, Fields and Particles (1990)
  • [172] AN Kirillov, NY Reshetikhin, Representations of the algebra Uq (sl (2)), q-orthogonal polynomials and invariants of links, Infinite dimensional Lie algebras and groups, 7, 285-339 (1989)
  • [173] PP Kulish, NY Reshetikhin, Universal-matrix of the quantum superalgebra osp(2 | 1), Letters in Mathematical Physics, 18, 143-149 (1989)
  • [174] G Moore, N Reshetikhin, A comment on quantum group symmetry in conformal field theory, Nuclear Physics B, 328(3), 557-574 (1989)
  • [175] LD Faddeev, Quantum groups, Boletim da Sociedade Brasileira de Matemática-Bulletin/Brazilian … (1989)
  • [176] NY Reshetikhin, Quasitriangular Hopf algebras and invariants of links, Algebra i Analiz, 1(2), 169-188 (1989)
  • [177] AG Izergin, VE Korepin, NY Reshetikhin, Conformal dimensions in Bethe ansatz solvable models, Journal of Physics A: Mathematical and General, 22(13) (1989)
  • [178] NY Reshetikhin, Calculation of the norm of Bethe vectors in models with SU (3)-symmetry, Journal of Soviet Mathematics, 46, 1694-1706 (1989)
  • [179] AN Kirillov, NY Reshetikhin, VG Kac, Infinite dimensional Lie algebras and groups, Advanced Series in Mathematical Physics, 7, 285-339 (1989)
  • [180] LD Faddeev, NY Reshetikhin, LA Takhtajan, Leningrad Math. J., 1, 193 (1990), Alg. Anal, 1 (1989)
  • [181] AG Izergin, VE Korepin, NY Reshetikhin, Field correlation functions in a one-dimensional Bose gas, Journal of Soviet Mathematics, 46, 1581-1588 (1989)
  • [182] NY Reshetikhin, MA Semenov-Tian-Shansky, Quantum R-matrices and factorization problems, Journal of Geometry and Physics, 5(4), 533-550 (1988)
  • [183] SV Kerov, AN Kirillov, NY Reshetikhin, Combinatorics, Bethe Ansatz, and representations of the symmetric group, Journal of Soviet Mathematics, 41, 916-924 (1988)
  • [184] LD Faddeev, NY Reshetikhin, LA Takhtajan, Quantization of Lie groups and Lie algebras, in Algebraic Analysis, Academic Press, 1, 129-139 (1988)
  • [185] N Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and inveriants of links: I, II, preprints LOMI E-4-87, E-17-87 (1988)
  • [186] NY Reshetikhin, Lomi preprints E-4-87, E-17-87 (1988)
  • [187] AN Kirillov, NY Reshetikhin, Properties of kernels of integral equations in XXZ models of arbitrary spin, Journal of Soviet Mathematics, 40, 35-71 (1988)
  • [188] NY Reshetikhin, Bethe-ansats for$SO(N)$-invariant transfermatrices, Zapiski Nauchnykh Seminarov POMI, 169, 122-140 (1988)
  • [189] AN Kirillov, NY Reshetikhin, Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin, Journal of Soviet Mathematics, 40, 22-35 (1988)
  • [190] NY Reshetikhin, LOMI preprints E-4-87 and E-17-87, Leningrad (1988)
  • [191] AN Kirillov, NY Reshetikhin, Multiplicity of weights in irreducibile tensor representations of a complete linear superalgebra, Functional Analysis and Its Applications, 22(4), 328-330 (1988)
  • [192] LD Faddeev, NY Reshetikhin, LA Takhtajan, RT, T₂= T₂T, R, Algebraic Analysis: Papers Dedicated to Professor Mikio Sato on the Occasion … (1988)
  • [193] L Fadeev, NY Reshetikhin, LA Takhtajan, Quantization of Lie groups and Lie algebras, Algebr. Analiz., 1, 178-206 (1987)
  • [194] AN Kirillov, NY Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. I. The ground state and the excitation spectrum, Journal of Physics A: Mathematical and General, 20(6) (1987)
  • [195] NY Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links, 1 (1987)
  • [196] E Ogievetsky, N Reshetikhin, P Wiegmann, The principal chiral field in two dimensions on classical lie algebras: the Bethe-ansatz solution and factorized theory of scattering, Nuclear Physics B, 280, 45-96 (1987)
  • [197] NY Reshetikhin, The spectrum of the transfer matrices connected with Kac-Moody algebras, letters in mathematical physics, 14, 235-246 (1987)
  • [198] NM Bogoliubov, AG Izergin, NY Reshetikhin, Finite-size effects and infrared asymptotics of the correlation functions in two dimensions, Journal of Physics A: Mathematical and General, 20(15) (1987)
  • [199] NY Reshetikhin, PB Weigmann, Towards the classification of completely integrable quantum field theories (the Bethe-ansatz associated with Dynkin diagrams and their automorphisms), Physics Letters B 189 (1-2), 125-131 (1987)
  • [200] AN Kirillov, NY Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin. II. Thermodynamics of the system, Journal of Physics A: Mathematical and General, 20(6) (1987)
  • [201] AG Izergin, VE Korepin, NY Reshetikhin, Correlation functions in a one-dimensional Bose gas, Journal of Physics A: Mathematical and General, 20(14) (1987)
  • [202] AN Kirillov, NY Reshetikhin, Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras, Zapiski Nauchnykh Seminarov POMI, 160, 211-221 (1987)
  • [203] LD Faddeev, NY Reshetikhin, Integrability of the principal chiral field model in 1+ 1 dimension, Annals of Physics, 167(2), 227-256 (1986)
  • [204] SV Kerov, AN Kirillov, NY Reshetikhin, Combinatorics Bethe ansats and representations of symmetric group, Zapiski Nauchnykh Seminarov POMI, 155, 50-64 (1986)
  • [205] AN Kirillov, NY Reshetikhin, Exact solution of the Heisenberg XXZ model of spin s, Journal of Soviet Mathematics, 35, 2627-2643 (1986)
  • [206] AN Kirillov, NY Reshetikhin, Bethe ansatz and combinatorics of Young tableaux, Zapiski Nauchnykh Seminarov POMI, 155, 65-115 (1986)
  • [207] PP Kulish, NY Reshetikhin, GL-invariant solutions of the Yang-Baxter equation and associated quantum systems, Journal of Soviet Mathematics, 34, 1948-1971 (1986)
  • [208] NY Reshetikhin, Calculation of Bethe vector norms for models with SU (3) symmetry, Problems of quantum field theory and statistical physics. 6 (1986)
  • [209] NM Bogolyubov, AG Izergin, NY Reshetikhin, Finite-dimensional effects and critical indices of one-dimensional quantum models, Pis' ma Zh. Eksp. Teor. Fiz., 44(9) (1986)
  • [210] NM Bogolyubov, AG Izergin, NY Reshetikhin, Finite-size effects and critical indices of 1D quantum models, Soviet Journal of Experimental and Theoretical Physics Letters, 44 (1986)
  • [211] AG Izergin, VE Korepin, NY Reshetikhin, Field carrelation functions for the one-dimensional Bose gas, Zapiski Nauchnykh Seminarov POMI, 150, 26-36 (1986)
  • [212] NM Bogolyubov, AG Izergin, NY Reshetikhin, fm= a+(1rc/6U) T2+ om).(4, JETP Lett, 44(9) (1986)
  • [213] NY Reshetikhin, Integrable models of quantum one-dimensional magnets with O (n) and Sp (2k) symmetry, Theor. Math. Phys., 63(3) (1985)
  • [214] NY Reshetikhin, O (N) invariant quantum field theoretical models: Exact solution, Nuclear Physics B, 251, 565-580 (1985)
  • [215] NY Beshetikhin, Hamiltonian structures for integrable field theory models. II. Models with O (n) and Sp (2k) symmetry on a one-dimensional lattice, Theor. Math. Phys., 63(2) (1985)
  • [216] AN Kirillov, NY Reshetikhin, Exact solution of the XXZ Heisenberg model of spin S, Zapiski Nauchnykh Seminarov POMI, 145, 109-133 (1985)
  • [217] AN Kirillov, NY Reshetikhin, A classification of string solutions of the Bethe equations for the XXZ model of arbitrary spin, Zapiski Nauchnykh Seminarov POMI, 146, 31-46 (1985)
  • [218] NY Reshetikhin, Hamiltonian structures for models of integrable field theory. 2. Models with O (n) and Sp (2k) symmetry on one-dimensional lattice, Teor. Mat. Fiz., 63(2) (1985)
  • [219] NY Reshetikhin, Exactly solvable quantum-mechanical systems on lattices associated with classical Lie algebras, Journal of Soviet Mathematics, 28, 539-549 (1985)
  • [220] N RESHETIKHIN, Modèles intégrables de mgnétiques quantiques unidimensionnels à symétrie O (n) et Sp (2k), Teoretičeskaâ i matematičeskaâ fizika, 63(3), 347-366 (1985)
  • [221] AN Kirillov, NY Reshetikhin, On the properties of integral kernels for the XXZ–model of arbitrary spin, Zapiski Nauchnykh Seminarov POMI, 146, 47-91 (1985)
  • [222] N RESHETIKHIN, Structures hamiltoniennes pour les modèles intégrables de la théorie du champ. II. Modèles à symétrie O (n) et Sp (2k) sur un réseau unidimensionnel, Teoretičeskaâ i matematičeskaâ fizika, 63(2), 197-207 (1985)
  • [223] PP Kulish, NY Reshetikhin, Integrable fermion chiral models, connected with the classical Lie algebras, Zapiski Nauchnykh Seminarov POMI, 133, 146-159 (1984)
  • [224] LD Faddeev, NY Reshetikhin, Integrability of a master chiral quantum field model (1984)
  • [225] PP Kulish, NY Reshetikhin, Quantum linear problem for the sine-Gordon equation and higher representations, Journal of Soviet Mathematics, 23, 2435-2441 (1983)
  • [226] PP Kulish, NY Reshetikhin, Diagonalisation of GL (N) invariant transfer matrices and quantum N-wave system (Lee model), Journal of Physics A: Mathematical and General, 16(16) (1983)
  • [227] NY Reshetikhin, A method of functional equations in the theory of exactly solvable quantum systems, Letters in Mathematical Physics, 7, 205-213 (1983)
  • [228] NY Reshetikhin, The functional equation method in the theory of exactly soluble quantum systems, Zh. Eksp. Teor. Fiz., 84(1), 190-1201 (1983)
  • [229] VI Vichirko, NY Reshetikhin, Excitation spectrum of the anisotropic generalization of an SU3 magnet, Theoretical and Mathematical Physics, 56(2), 805-812 (1983)
  • [230] NY Reshetikhin, LD Faddeev, Hamiltonian structures for integrable models of field theory, Teoreticheskaya i Matematicheskaya Fizika, 56(3), 323-343 (1983)
  • [231] NY Reshetikhin, LD Faddeev, Hamiltonian structures of the integrable field theory models, Teor. Mat. Fiz., 56(3) (1983)
  • [232] NY Reshetikhin, FA Smirnov, Quantum Floquet functions, Zapiski Nauchnykh Seminarov POMI, 131, 128-141 (1983)
  • [233] NY Reshetikhin, Exactly solvable quantum-meehanical systems on the lattices associated with the classical Lie algebras, Zapiski Nauchnykh Seminarov POMI, 123, 112-125 (1983)
  • [234] VI VICHIRKO, N RESHETIKHIN, Spectre des excitations de la généralisation anisotrope du SV3-magnétique, Teoretičeskaâ i matematičeskaâ fizika, 56(2), 260-271 (1983)
  • [235] N RESHETIKHIN, LD FADDEEV, Structures hamiltoniennes pour les modèles intégrables de la théorie du champ, Teoretičeskaâ i matematičeskaâ fizika, 56(3), 323-343 (1983)
  • [236] PP Kulish, NY Reshetikhin, On$GL_3$-invariant solutions to the Yang–Baxter equation and the assosiated quantum systems, Zapiski Nauchnykh Seminarov POMI, 120, 92-121 (1982)
  • [237] PP Kulish, NY Reshetikhin, EK Sklyanin, Yang-Baxter equation and representation theory: I, Letters in Mathematical Physics, 5, 393-403 (1981)
  • [238] PP Kulish, NY Reshetikhin, Generalized Heisenberg ferromagnet and the Gross-Neveu model, Sov. Phys. JETP, 53(1), 108-114 (1981)
  • [239] PP Kulish, NY Reshetikhin, Zapiski Nauchnykh Seminarov LOMI (1981)
  • [240] Nicolai Reshetikhin, Ananth Sridhar, Limit Shapes of the Stochastic Six Vertex Model, accepted in Communications in Mathematical Physics, arXiv:1609.01756
  • [241] OG Iosifovich, PF Vladimirovich, TN Vladimirovna, MA Valer'evich et al., New Perspectives in Asymptotic Representation Theory. In memory of Sergei Kerov (1946–2000)
  • [242] IY Sergeevich, KA Vladimirovich, SA Bronislavovich, TM Anatol'evich et al., Globus Seminar
  • [243] NY RESHETIKHIN, AND THEIR AUTOMORPHISMS
  • [244] NY Reshetikhin, A survey on the problems of deformation quantization
  • [245] NY Reshetikhin, On superintegrability
  • [246] NY Reshetikhin, On multiplicities of irreducible components in large tensor powers of representations of simple Lie groups
  • [247] NY Reshetikhin, On stratified structure of integrable dynamics
  • [248] NY Reshetikhin, On tensor powers of representations of quantum groups at roots of unity
  • [249] NY Reshetikhin, Integrable systems on moduli spaces of flat connections over surfaces
  • [250] N Reshetikhin, Poisson sigma model and quantum mechanics
  • [251] N Reshetikhin, On invariants of links with flat connection in the complement
  • [252] N Reshetikhin, On the semiclassical limit of solvable lattice models
  • [253] NY Reshetikhin, Spin Calogero-Moser system and two dimensional Yang-Mills theory with corners
  • [254] N RESHETIKHIN, Modèles intégrables de mgnétiques quantiques unidimensionnels à symétrie O (n) et Sp (2k) Integrable models of one-dimensional quantum magnetics with the O (n) and Sp (2k) symmetry
  • [255] VI VICHIRKO, N RESHETIKHIN, Spectre des excitations de la généralisation anisotrope du SV 3-magnétiqueExcitation spectrum of anisotropic generalization of SU (3)-ferromagnet
  • [256] EH Lieb, M Aizenman, JL Lebowitz, D Ruelle, IVL Flato, J Simon, E Taflin et al., Springer International,
  • [257] M Herman, PJL Lebowitz, NY Reshetikhin, YG Sinai, T Spencer et al., Chief Editor A. Jaffe, Cambridge, MA Editorial Board M. Aizenman, Princeton, NJ H. Araki, Kyoto A. Connes, Bures-sur-Yvette R. Dijkgraaf, Amsterdam
  • [258] M Sato, F Pham, BM McCoy, I Cherednik, H McKean, V Lakshmibai et al., Hayashibara Forum 1990 International Symposium on Special Functions
  • [259] V Chari, G Cliff, P Littelmann, N Reshetikhin, Representations of Kac-Moody Algebras and Combinatorics
  • [260] M Baig, A Cuervo, A Billoire, F David, M BOhm, A Denner, DV Boulatov et al., Papers to appear in forthcoming issues of Nuclear Physics BIFS
  • [261] N Reshetikhin, M Haiman, M Aganagic, O Ganor, Qualifying Exam Syllabus
  • [262] M Baig, A Cuervo, KA Benedict, Y Brihaye, P Spindel, M Creutz, R Gavai et al., Papers to appear in forthcoming issues of Nuclear Physics B [FS]

 

更新时间: 2025-07-26 13:00:05