BIMSA > Anatoli Kirillov
Professor Anatoli Kirillov

Group: Algebraic Geometry

Office: A3-1-205

Email: kirillov@bimsa.cn

Research Field: Representation theory, Algebraic Combinatorics, Tropical Combinatorics, Algebraic Geometry, Special Functions, Exactly Solvable Models

Webpage: https://www.kurims.kyoto-u.ac.jp/~kirillov

Biography

Anatol Kirillov is a researcher in the area of integrable systems, representation theory, special functions, algebraic combinatorics, and algebraic geometry. He worked as a professor in different universities in Japan for the last 20 years. In 2022 he joined BIMSA as a research fellow.

Research Interest

  • Representation theory (Classical groups, Kac-Moody algebras and groups, Quantum groups, Hecke algebras)
  • Algebraic Combinatorics (Symmetric functions, Young tableaux, Rigged configurations, Yang-Baxter equations, Bracket algebras, Schubert calculus)
  • Tropical Combinatorics (Gelfand-Tsetlin patterns, Crystal basis, Convex polytops, Toric varieties, Continious analog of Robinson-Schensted-Knuth correspondence)
  • Algebraic Geometry (Artin-Mazur formal groups, Mixed Hodge structures, Quantum cohomology, Quantum Schubert calculus)
  • Special Functions (Clebsch-Gordan and Racah-Wigner coefficients, generalized Hypergeometric functions, Quantum polylogarithms)
  • Exactly Solvable Models (Bethe ansatz, Formfactors, Dilogarithm identities, Bosonic and Fermionic formulae for characters and branching functions)

Education Experience

  • 1971 - 1975      Leningrad SU, Russia
  • - 1988      LOMI, Lenengrad      Doctor      Hb.D
  • - 1986      LOMI, Lenenfrad      Doctor

Work Experience

  • 2022 -      BIMSA      Professor
  • 2001 - 2022      RIMS,Kyoto,Japan      Professor
  • 1998 - 2001      Nagoya University      Professor
  • 1993 - 1998      U. Wisconsin      Professor
  • 1971 - 1993      LOMI, Leningrad      Researcher

Publication

  • [1] Anatol Kirillov, Gleb Nenashev, Boris Shapiro, Arkady Vaintrob, Bizonotopal Graphical Algebras, arXiv preprint arXiv:2407.19431 (2024)
  • [2] A. Kirillov, G. Nenashev, On Q-deformations of Postnikov-Shapiro algebras, Niminaire Lotharingien de Combinatoire, 78B (2017), Article n.55, 12 pp.
  • [3] A.Berenstein, A. Kirillov, Cactus group and Gelfand--Tsetlin group, Preprint RIMS-1858, 2016.
  • [4] A.P. Isaev, A. Kirillov, V.O. Tarasov, Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations, arXiv preprint arXiv:1510.05374, 49 (2015)
  • [5] A. Kirillov, R. Sakamoto, Bethe's Quantum Numbers And Rigged Configurations, Nuclear Physics B 905 (2016), 359--372, doi:10.1016/j.nuclphysb.2016.02.020 ; Preprint RIMS-1834, 2015, arXiv:1509.02305.
  • [6] A. Kirillov, Rigged Configurations and Catalan, Stretched Parabolic Kostka Numbers and Polynomials : Polynomiality, Unimodality and Log-concavity (2015)
  • [7] A. Kirillov, H. Naruse, Construction of double Grothendieck polynomials of classical types using Id-Coxeter algebras, Preprint RIMS-1823, 2015, arXiv:1504.08089.
  • [8] A. Kirillov, On Double Schubert and Grothendieck polynomials for Classical Groups, Preprint RIMS-1820, 2015, arXiv:1504.01469.
  • [9] A. Kirillov, On some quadratic algebras I+I/2 : Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and Reduced polynomials, SIGMA 12(2016) 002, 172 pages; Preprint RIMS-1817, 2015, arXiv:1502.00426.
  • [10] A. Kirillov, Notes on Schubert, Grothendieck and Key polynomials, SIGMA 12 (2016) 037, 56 pages, Preprint RIMS-1815, 2015, arXiv:1501.07337.
  • [11] A. Kirillov, R. Sakamoto, Some Remarks On Nepomechie--Wang Eigenstates For Spin 1/2 XXX Model, arXiv preprint arXiv:1406.1958, 15, 1-16 (2014)
  • [12] A. Kirillov, R. Sakamoto, Singular solutions to the Bethe ansatz equations and rigged configurations, Journal of Physics A: Mathematical and Theoretical, 47(20), 205207 (2014)
  • [13] A. Isaev, A. Kirillov, Bethe subalgebras in Hecke algebra and Gaudin models, Letters in Mathematical Physics, 104, 179-193 (2014)
  • [14] A. Kirillov, On some algebraic and combinatorial properties of Dunkl elements, International Journal of Modern Physics B, 26(27n28), 1243012 (2012)
  • [15] A. Kirillov, T. Maeno, Affine nil-Hecke algebras and braided differential structure on affine Weyl groups, Publications of the Research Institute for Mathematical Sciences, 48(1), 215-228 (2012)
  • [16] A. Kirillov, On some combinatorial and algebraic properties of Dunkl elements RIMS Kokyuroku, 1795, 1-44, Kyoto University, 2012
  • [17] A. Kirillov, On some algebraic and combinatorial properties of Dunkl elements, International Journal of Modern Physics B, 26 (2012), No. 27n28
  • [18] A. Kirillov, H. Katsura, N. Kawashima, V. Korepin, S. Tanaka, Entanglment in valence-bond-solid states on symmetric graphs, J. Phys. A 43 (2010), no.255303, 28p.
  • [19] A. Kirillov, T.Maeno, Nichols-Woronowicz model of coinvariant algebra of complex reflection groups, J. Pure Appl. Algebra 214 (2010), 402-409
  • [20] A. Kirillov, R. Sakamoto, Relationships between two approaches: rigged configurations and 10-eliminations, Letters in Mathematical Physics, 89, 51-65 (2009)
  • [21] A. Kirillov, R. Sakamoto, Paths and Kostka-Macdonald polynomials, Moscow Math. Journal, 9(2009), 823-854 (2009)
  • [22] A. Kirillov, T.Maeno, Wonderful Amoebas, Sugaku 58 (2006), 151-164, translation in Sugaku Expositions 22 (2009), 107-120
  • [23] A. Kirillov, T. Maeno, Braided differential structure on Weyl groups, quadratic algebras, and elliptic functions, International Mathematics Research Notices, 2008(9), rnn046-rnn046 (2008)
  • [24] Feigin B., A. Kirillov, Loktev S., Combinatorics and geometry of higher level Weyl modules, arXiv preprint math/0503315, 221, 33-47 (2005)
  • [25] A. Kirillov, T.Maeno, Exterior differential algebras and flat connections on Weyl groups, , 81(2), 30-35 (2005)
  • [26] A. Kirillov, T.Maeno, On some noncommutative algebras related with K-theory of flag varieties, IRMN 60 (2005), 3753-3789, Preprint RIMS, 2005, 25p. math.CO/0504290
  • [27] K.Hikami, A. Kirillov, Hypergeometric generating function of L-function, Slater's identities and Quantum invariant, Algebra i Analiz 17 (2005), no.1, 190-208, Preprint RIMS-1463, 2004, 18p. math-ph/0406042
  • [28] A. Kirillov, An invitation to the generalized saturation conjecture, Publications of the Research Institute for Mathematical Sciences, 40(4), 1147-1239 (2004)
  • [29] A. Kirillov, T.Maeno, A note on quantization on Nichols algebra model for Schubert calculus on Weyl groups, Lett. in Math. Phys. 72 (2005) 233-241, Preprint RIMS-1481, 2004, 8p. math.QA/0412069
  • [30] A. Kirillov, T.Maeno, Noncommutative algebras related with Schubert calculus on Coxeter groups, European Journal of Combinatorics, 25 (2004), 1301-1325, Preprint RIMS-1437, 2003, 23p. math.CO/0310068
  • [31] K.Hikami, A. Kirillov, Torus knot and minimal model, Physics Letters B 575 (2003), 343-348, hep-th/0308152, 2003, 10p.
  • [32] A. Kirillov, M.Taneda, Generalized Umemura polynomials, The Rocky Mountain journal of mathematics, 32, 691-702 (2002)
  • [33] A. Kirillov,A.Schilling,M.Shimozono, A bijection between Littlewood-Richardson tableaux and rigged configurations, Selecta Mathematica, 8(1), 67 (2002)
  • [34] A. Kirillov, M.Taneda, Generalized Umemura polynomials and the Hirota-Miwa equations, MathPhys Odyssey 2001: Integrable Models and Beyond, 23, 313-332 (2002)
  • [35] A. Kirillov, Introduction to Tropical Combinatorics, Physics and Combinatorics 2000 (Proceedings of the Nagoya 2000 International Workshop on Physics and Combinatorics, Nagoya University, August 21-26, 2000, ed. A.Kirillov and N.Liskova), 82-150, World Scientific, Singapore, 2001
  • [36] A.Kirillov, A.Tsuchiya, H.Umemura, a Remark on the Harish-Chandra Series for Hyperboloids, , 11-15 (2001)
  • [37] A.Kirillov, A.Tsuchiya, H.Umemur, Ubiquity of Kostka polynomials, , 85-200 (2001)
  • [38] J.F. van Diejen, A.Kirillov, Determinantal formulas for zonal spherical functions of hyperboloids, Mathematische Annalen, 319(2), 215-234 (2001)
  • [39] A.Kirillov, Combinatorics of Young tableaux and rigged configurations (Russian), Proceedings of the St.Petersburg Math. Soc., 7((1999)), 23-115; translation in Proceedings of the St.Petersburg Math. Soc. Volume VII, Amer. Math. Soc. Transl. Ser.2, 203, 17-98, AMS, Providence, RI (2001)
  • [40] A.Kirillov, Bijectives correspondances for rigged configurations (Russian), Algebra i Analiz, 12(2000), 204-240, translation in St.Petersburg Math. J. 12 (2001), no.1, 161-190 (2001)
  • [41] A.Kirillov, A.Schilling and M.Shimozono, Various representations of the generalized Kostka polynomials, The Andrews Festschrift, Seventeen Papers on Classical Number Theory and Combinatorics (eds. D.Foata and G.-N.Han), 209-226, Springer, 2001 and Seminaire Lotharingien de Combinatoire 42 (1999), 19pp.
  • [42] A.Berenstein, A.Kirillov, Domino tableaux, Schützenberger involution, and the symmetric group action, Discrete Mathematics, 225(1-3), 15-24 (2000)
  • [43] J.F. van Diejen, A.Kirillov, Formulas for-Spherical Functions Using Inverse Scattering Theory of Reflectionless Jacobi Operators, Communications in Mathematical Physics, 210, 335-369 (2000)
  • [44] J.F. van Diejen, A.Kirillov, A combinatorial formula for the associated Legendre functions of integer degree, Advances in Mathematics, 149(1), 61-88 (2000)
  • [45] A. Kirillov, N.A. Liskova, Bethe's states for generalized XXX and XXZ models, Physics and Combinatorics 2000 (Proceedings of the Nagoya 2000 International Workshop on Physics and Combinatorics, Nagoya University, August 21-26, 2000, ed. A.Kirillov and N.Liskova), 151-163, World Scientific, Singapore, 2001. math.QA/0103030
  • [46] A.Kirillov, Some remarkable quadratic algebras and Schubert Calculus, Proceedings of the 45-th Symposium on Algebra, 45(8), 142-151 (2000)
  • [47] A.Kirillov, On some quadratic algebras, L.D. Faddeev's Seminar on Mathematical Physics, 91-113, American Mathematical Society Translations: Series 2 201, AMS, Providence, RI, 2000, q-alg/9705003
  • [48] A.Kirillov, T.Maeno, Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula, Proceedings of the 9th International Conference on Formal Power Series and Algebraic Combinatorics(301-312) (2000)
  • [49] A.Kirillov, On some quadratic algebras: Jucys-Marphy and Dunkl elements, Calogero-Moser-Sutherland models, (Montreal, PQ, March 10-15, 1997) CRM Series in Mathematical Physics, 231-248 (2000)
  • [50] A.Kirillov, t-Deformations of quantum Schubert polynomials, Funkcialaj Ekvacioj, 43, 57-69 (2000)
  • [51] A.Kirillov, Quantum Schubert polynomials and quantum Schur functions, International Journal of Algebra and Computation, 9(03n04), 385-404 (1999)
  • [52] A.Kirillov, Quantum Grothendieck polynomials, Algebraic methods and q-special functions (Montréal, QC, 1996), 22, 215-226 (1999)
  • [53] A.Kirillov, M.Noumi, q-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients, Algebraic Methods and q-Special Functions, CRM Proc. Lecture Notes 22, 227-243 (1999)
  • [54] A.Kirillov, A.Schilling, M.Shimozono, On a bijection between Littlewood-Richardson tableaux and rigged configurations, Proceedings of the 11th International Conference on Formal Power Series and Algebraic Combinatorics, 266-274 (1999)
  • [55] G.Hatayama, A.Kirillov, A.Kuniba, M.Okado, T.Takagi and Y.Yamada, Character formulae of sl_n modules and inhomogeneous paths, Nucl. Phys. B 536 (1999), 575-616, math.QA/9802085
  • [56] S.Fomin, A.Kirillov, Quadratic algebras, Dunkl elements, and Schubert calculus, Advances in geometry, 147, 147-182 (1999)
  • [57] A.Kirillov, M.Noumi, Affine Hecke algebras and raising operators for Macdonald polynomials, , 93(1), 1-39 (1998)
  • [58] A. Kirillov, M.Shimozono, A generalization of the Kostka-Foulkes polynomials, arXiv preprint math/9803062, 15, 27-69 (1998)
  • [59] A.Kirillov, New combinatorial formula for modified Hall-Littlewood polynomials, q-Series from a Contemporary Perspective (AMS-ISM-SIAM Joint Summer Research Conference on q-series, Combinatorics, and computer Algebra; June 21-25, 1998, Mount Holyoke, MA, USA), 283-333, Contemporary Mathematics 254, AMS, Providence, RI, 2000, math.QA/9803006
  • [60] A.Kirillov, A.Kuniba and T.Nakanishi, Skew Young diagram method in spectral decomposition of integrable lattice models II, Higher levels, Nucl. Phys. B 529 (1998), 611-638, q-alg/9711009
  • [61] A.Berenstein, A.Kirillov, Domino tableaux, Schutzenberger involution and action of the symmetric group, Proceedings of the 10th International Conference on Formal Power Series and Algebraic Combinatorics, Fields Institute, Toronto, 1998, 55-66. q-alg/9709010
  • [62] S.Fomin, A.Kirillov, Reduced words and plane partitions, Journal of Algebraic Combinatorics, 6(4), 311-319 (1997)
  • [63] A. Kirillov, Cauchy identities for universal Schubert polynomials, arXiv preprint q-alg/9703047, 283, 123-139 (1997)
  • [64] A. Kirillov, Skew divided difference operators and Schubert polynomials, J. Pure Appl. Algebra SIGMA 3 (2007) 072, 14 pages, Preprint CRM-2526, 1997, 15p.; q-alg/9712053
  • [65] A.Kirillov, T.Maeno, Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula, Proceedings of the 9th International Conference on Formal Power Series and Algebraic Combinatorics, Wien, July 14-July 18, 1997, 301-312.
  • [66] A.Kirillov, A.Kuniba and T.Nakanishi, Skew Young diagram method in spectral decomposition of integrable lattice models, Comm. Math. Phys. 185 (1997), no.2, 441-465. q-alg/9607027
  • [67] A.Kirillov, N.A.Liskova, Completeness of Bethe's states for generalized XXZ model, J. Phys. A 30 (1997), no.4, 1209-1226. hepth/9407107
  • [68] S.Fomin, A.Kirillov, Universal exponential solution of the Yang-Baxter equation, Letters in Mathematical Physics, 37, 273-284 (1996)
  • [69] S.Fomin, A.Kirillov, Combinatorial $B_n$-analogues of Schubert polynomials, Transactions of the AMS, 348(1996), 3591-3620 (1996)
  • [70] S.Fomin, A.Kirillov, The Yang-Baxter equation, symmetric functions, and Schubert polynomials, Discrete Mathematics 153 (1996), 123-143.
  • [71] A.Berenstein, A.Kirillov, Group generated by involutions, Gelfand-Tsetlin patterns and combinatorics of Young tableaux, Algebra i Analiz 7 (1995), no.1, 7(1), 92-152 (1996)
  • [72] A.Kirillov, Dilogarithm identities, Progress of theoretical physics supplement, 118, 61-142 (1995)
  • [73] A.Kirillov, Dilogarithm identities, Lectures in Mathematical Sciences the University of Tokyo, 7 (1995), 96p.
  • [74] S.Fomin, A.Kirillov, Grothendieck polynomials and the Yang-Baxter equation, Proc. formal power series and alg. comb, 1994, 183-190 (1994)
  • [75] A.Kirillov, A.Lascoux, B.Leclerc and J.-Y.Thibon, S駻ies g駭駻atrices pour les tableaux de dominos (French), C.R. Acad. Sci. Paris Ser. I 318 (1994), no.5, 395-400.
  • [76] A.Kirillov, Dilogarithm identities, partitions and spectra in conformal field theory, Part I, Algebra i Analiz 6 (1994), no.2, 152-175.
  • [77] A.Kirillov, Dilogarithm identities and spectra in conformal field theory, , 99-108 (1993)
  • [78] A.Kirillov, Generalization of the Gale-Ryser theorem, arXiv preprint hep-th/9304099, 21, 1047-1055 (1993)
  • [79] A.Kirillov, N.Yu.Reshetikhin, Formulae for the multiplicites of the occurrence of irreducible components in the tensor product of representations of simple Lie algebras (Russian), Zap. Nauch. Sem. LOMI 205 (1993), 30-37, translation in Journal of Mathematical Sciences 80, no.3 (1996), 1768-1772
  • [80] A.Kirillov, P.Mathieu, L.B馮in, M.A.Walton, Berenstein-Zelevinski triangles, elementary couplings and fusion rules, Lett. in Math. Phys. 28 (1993), no.4, 257-268.
  • [81] S.Fomin, A.Kirillov, The Yang-Baxter equation, symmetric functions and Schubert polynomials, Proceedings of the 5th International Conference on Formal Power Series and Algebraic Combinatorics(215-230) (1993)
  • [82] A.Kirillov, P.Mathieu, D.Senechal, M.A.Walton, Can fusion coefficients be calculated from the depth rule ?, Nucl. Phys. B, 391(no.3), 651-674 (1993)
  • [83] A.Kirillov, Unimodality of generalized Gaussian coefficients, arXiv preprint hep-th/9212152, 315, 497-501 (1992)
  • [84] A.Kirillov, P.Mathieu, D.Senechal, M.A.Walton, Crystallizing the depth rule for WZNW fusion coefficients, Proceedings of the XIXth International Colloquium on Group Theoretical Physics (1992)
  • [85] S.V.Kerov, A.Kirillov, Combinatorics of rational representations of the group GL(n,C), 200(3), 83-93 (1992)
  • [86] A.Kirillov, N.A.Liskova, Clebsch-Gordan and Racah-Wigner coefficients for $U_q(SU(1,1))$, Int. Jour. Mod. Phys. A, 7(1-2), 611-621 (1992)
  • [87] A.Kirillov, Decomposition of symmetric and exterior powers of the adjoint representation of $hbox{germ g}l(N)$. 1. Unimodality of principal specialization of the internal product of the Schur functions, Int. Jour. Mod. Phys. A, 7(1-2), 545-579 (1992)
  • [88] A.Kirillov, The Lagrange identity and the hook formula (Russian), Zap. Nauch. Sem. LOMI, 172(1989), 78-87 (1992)
  • [89] A.Kirillov, Clebsch-Gordan quantum coefficients, Journal of Soviet Mathematics, 53, 264-276 (1991)
  • [90] A.Kirillov, On some properties of the Robinson-Schensted correspondence, Proceedings of Hayashibara conference on special functions, 122-126 (1990)
  • [91] A.Kirillov, Representation of quantum groups, combinatorics, q-orthogonal polynomials and link invariants (Russian), 300p. (1990)
  • [92] A.Kirillov, N.Yu.Reshetikhin, q-Weyl group and a multiplicative formula for universal R-matrices, Comm. Math. Phys., 134(1990), 316-325 (1990)
  • [93] A.Kirillov, V.E.Korepin, The resonating valence bond in quasicristals (Russian), Algebra i Analiz, 1(1989), 47-76, translation in Leningrad Math. J. 1 (1990), n.2, 343-377. (1990)
  • [94] A.Kirillov, N.Yu.Reshetikhin, Representations of the algebra $U_q(sl(2))$, q-orthogonal polynomials and invariants of links, Adv. Series in Math. Phys., 7(1989), 285-339 (1989)
  • [95] A.Kirillov, Identities for the Rogers dilogarithmic function connected with simple Lie algebras (Russian), Zap. Nauch. Sem. LOMI, 164(1987), 121-133, translation in Journal of Soviet Math. 47 (1989), 2450-2458. (1989)
  • [96] A.Kirillov, Formulas for formfactors in the quantum sinh-Gordon model, Zap. Nauch. Sem. LOMI, 164(1987), 54-66, translation in Journal of Soviet Math. 47 (1989), 2403-2412. (1989)
  • [97] A.Kirillov, F.A.Smirnov, Formfactors in the SU(2)-invariant Thirring model, Zap. Nauch. Sem. LOMI, 164(1987), 80-120, translation in Journal of Soviet Math 47 (1989), 2423-2449 (1989)
  • [98] A.Kirillov, On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers, Journ. Geom. and Phys., 5(1), 365-389 (1988)
  • [99] A.Kirillov, N.Yu.Reshetikhin, Multiplicity of weight in irreducible tensor representations of a complete linear syperalgebra (Russian), Funct. Anal. and Applicat., 22(4), 84-85 (1988)
  • [100] A.Kirillov, F.A.Smirnov, Form-factors in O(3) nonlinear $sigma$-model, Int. Jour. Mod. Phys. A, 3(no.3), 731-741 (1988)
  • [101] S.V.Kerov, A.Kirillov and N.Yu.Reshetikhin, Combinatorics, the Bethe ansatz and representations of the symmetric group (Russian), Zap. Nauch. Sem. LOMI 155 (1986), 50-64, translation in Journal of Soviet Math. 41 (1988), 916-924.
  • [102] A.Kirillov, N.Yu.Reshetikhin, The Bethe ansatz and the combinatorics of Young tableaux (Russian), Zap. Nauch. Sem. LOMI 155 (1986), 65-115, translation in Journal of Soviet Math. 41 (1988), 925-955.
  • [103] A.Kirillov, T-invariance, CPT-invariants and local commutativity of the quantum $(chvarphi)_2$ model (Russian), Zap. Nauch. Sem. LOMI, 146(1985), 9-19 (1988)
  • [104] A.Kirillov, V.E.Korepin, Norms of bound states, Zap. Nauch. Sem. LOMI, 146(1985), 20-30 (1988)
  • [105] A.Kirillov, N.Yu.Reshetikhin, Properties of kernels of integral equations in the XXZ-model of arbitrary spin (Russian), Zap. Nauch. Sem. LOMI, 146(1985), 47-91 (1988)
  • [106] A.Kirillov, F.A.Smirnov, Solution of some combinatorial problems arising in the calculation of correlators in exactly solvable models, Zap. Nauch. Sem. LOMI, 164(1987), 67-79, translation in Journal of Soviet Math. (1987)
  • [107] A.Kirillov, F.A.Smirnov, A representation of the current algebra connected with SU(2)-invariant Thirring model, Phys. Lett. B, 198(4), 506-510 (1987)
  • [108] A.Kirillov, N.Yu.Reshetikhin, The Bethe ansatz and the combinatorics of Young tableaux, Zap. Nauch. Sem. LOMI, 155(1986), 65-115 (1987)
  • [109] A.Kirillov, N.Yu.Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin, I, J. Phys. A 20 (1987), 1565-1586.
  • [110] A.Kirillov, N.Yu.Reshetikhin, Exact solution of the integrable XXZ Heisenberg model with arbitrary spin, II, J. Phys. A, 20(1587-1597) (1987)
  • [111] A.Kirillov, N.Yu.Reshetikhin, Quantum inhomogeneous XXZ magnet and non-linear $sigma$-models, Proceedings of Paris-Meudon Colloquium, Paris, 1987, 235-257 (1987)
  • [112] A.Kirillov, N.Yu.Reshetikhin, Representation of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras (Russian), Zap. Nauch. Sem. LOMI, 160(1987), 211-221 (1987)
  • [113] A.Kirillov, Some generalization of the Abjankar-Moh theorem (Russisn), Proceedings of Algebraic Conference, L'vov, 1987, part 1, p.131.
  • [114] A.Kirillov, Completeness of states of the generalized Heisenberg magnet (Russian), Zap. Nauch. Sem. LOMI, 134(1985), 169-189 (1987)
  • [115] A.Kirillov, Convex polytops and formal groups (Russian), Zap. Nauch. Sem. LOMI, 75(1978), 87-90 (1987)
  • [116] A.Kirillov, N.Yu.Reshetikhin, The Yangians, Bethe ansatz and combinatorics, letters in mathematical physics, 12, 199-208 (1986)
  • [117] A.Kirillov, Exact solution of XXZ-Heisenberg model of the higher spin (Russian), Zap. Nauch. Sem. LOMI, 145(1985), 109-133, 2627-2643 (1986)
  • [118] A.Kirillov, N.Yu.Reshetikhin, Classification of the string solutions of Bethe equations in the XXZ-model of arbitrary spin (Russian), Zap. Nauch. Sem. LOMI, 146(1985), 31-46 (1985)
  • [119] A.Kirillov, S.V.Vostokov, Norm pairing in a two-dimensional local field, Zap. Nauch. Sem. LOMI, 132(1983), 76-84, translation in Journal of Soviet Math. 30 (1985), 1847-1853 (1985)
  • [120] A.Kirillov, Combinatorial identities and completeness of states for the Heisenberg magnet (Russian), Zap. Nauch. Sem. LOMI, 131(1983), 88-105, translation in Journal of Soviet Math. 30 (1985), 2298-3310. (1985)
  • [121] A.Kirillov, The Zeta function of the monodromy of a singular point of complete intersection (Russian), Zap. Nauch. Sem. LOMI, 112(1981), 112-119, translation in Journal of Soviet Math. 25 (1984), 1051-1056. (1984)
  • [122] A.Kirillov, Mixed Hodge structure of the isolated singularity of the hypersuface, Shot Communications, p.34 (1982)
  • [123] A.Kirillov, Formula for calculating the integer cohomology of the link of an isolated hypersurface singularity (Russian), Zap. Nauch. Sem. LOMI, 100(1980), 106-112, translation in Journal of Soviet Math. 19 (1982), 1695-1699. (1982)
  • [124] A.Kirillov, Milnor's number of isolated singularity of complete intersection (Russian), Proceedings of Algebraic conference, Leningrad, 1981, part 1, p.97.
  • [125] A.Kirillov, Commutative formal groups (Russian), Zap. Nauch. Sem. LOMI, 57(117-124) (1979)
  • [126] M.I.Bashmakov, A.Kirillov, Lutz filtration of formal groups, Izv. Acad. of Scien. USSR, 139(6), 1227-1239 (1979)
  • [127] A.Kirillov, Classification of the formal O-modules, Proceedings of Algebraic conference, Krasnoyarsk(1977), 76 (1977)
  • [128] A KIRILLOV, G NENASHEV, B SHAPIRO, A VAINTROB, INTRODUCING BIZONOTOPAL ALGEBRAS FOR UNDIRECTED GRAPHS (2024)
  • [129] AN Kirillov, Rigged Configurations and Unimodality, Representation Theory, Mathematical Physics, and Integrable Systems: In … (2021)
  • [130] AN Kirillov, T Scrimshaw, Hook-content formula using excited Young diagrams, arXiv preprint arXiv:1904.00371 (2019)
  • [131] G Nenashev, A Kirillov, Unimodular Zonotopal Algebra (2018)
  • [132] AN Kirillov, H Naruse, Construction of double Grothendieck polynomials of classical types using idCoxeter algebras, Tokyo Journal of Mathematics, 39(3), 695-728 (2017)
  • [133] AN Kirillov, G Nenashev, On$Q$-deformations of Postnikov-Shapiro algebras, Preprint (2017)
  • [134] AN Kirillov, On some quadratic algebras I 1/2: combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 12 (2016)
  • [135] AN Kirillov, Notes on Schubert, Grothendieck and key polynomials, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 12 (2016)
  • [136] AN Kirillov, R Sakamoto, Bethe's quantum numbers and rigged configurations, Nuclear Physics B, 905, 359-372 (2016)
  • [137] A BERENSTAIN, AN KIRILLOV, RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES (2016)
  • [138] AN Kirillov, On Double Schubert and Grothendieck polynomials for classical groups, arXiv preprint arXiv:1504.01469 (2015)
  • [139] AN Kirillov, Rigged Configurations and Catalan, Stretched Parabolic Kostka Numbers and Polynomials: Polynomiality, Unimodality and Logconcavity, arXiv preprint arXiv:1505.01542 (2015)
  • [140] AN Kirillov, On some combinatorial and algebraic properties of Dunkl elements (Topics in Combinatorial Representation Theory), 数理解析研究所講究録, 1795, 1-44 (2012)
  • [141] S CALCULUS, S FOMIN, AN KIRILLOV, QUADRATIC ALGEBRAS, DUNKL ELEMENTS, Advances in Geometry, 1 (2012)
  • [142] S Tanaka, H Katsura, N Kawashima, AN Kirillov, VE Korepin, Entanglement Entropy in Valence-Bond-Solid States on Symmetric Graphs (New Development of Numerical Simulations in Low-Dimensional Quantum Systems: From Density Matrix …, 物性研究, 95(6), 625-625 (2011)
  • [143] A Kirillov, T Maeno, Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties, St. Petersburg mathematical journal, 22(3), 447-462 (2011)
  • [144] H Katsura, N Kawashima, AN Kirillov, VE Korepin, S Tanaka, Entanglement in valence-bond-solid states on symmetric graphs, Journal of Physics A: Mathematical and Theoretical, 43(25) (2010)
  • [145] AN Kirillov, T Maeno, Nichols–Woronowicz model of coinvariant algebra of complex reflection groups, Journal of Pure and Applied Algebra, 214(4), 402-409 (2010)
  • [146] AN Kirillov, R Sakamoto, Generalized Energy Statistics and Kostka―Macdonald Polynomials, Discrete Mathematics & Theoretical Computer Science (2010)
  • [147] AN Kirillov, VE Korepin, The valence bond solid in quasicrystals, arXiv preprint arXiv:0909.2211 (2009)
  • [148] AN Kirillov, R Sakamoto, Paths and Kostka--Macdonald Polynomials, arXiv preprint arXiv:0811.1085 (2008)
  • [149] AN Kirillov, Skew divided difference operators and Schubert polynomials, SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 3 (2007)
  • [150] A Kirillov, 放物型コストカ多項式, えびら多様体, 結晶基底とトロピカル組み合わせ論, 京都大学 (2006)
  • [151] K Hikami, A Kirillov, Hypergeometric generating function of 𝐿-function, Slater’s identities, and quantum invariant, St. Petersburg Mathematical Journal, 17(1), 143-156 (2006)
  • [152] AN Kirillov, T Maeno, A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups, Letters in Mathematical Physics, 72, 233-241 (2005)
  • [153] AN Kirillov, T Maeno, On some noncommutative algebras related to K-theory of flag varieties. Part I, International Mathematics Research Notices, 60, 3753-3789 (2005)
  • [154] AN Kirillov, T Maeno, Noncommutative algebras related with Schubert calculus on Coxeter groups, European Journal of Combinatorics, 25(8), 1301-1325 (2004)
  • [155] K Hikami, AN Kirillov, Torus knot and minimal model, Physics Letters B 575 (3-4), 343-348 (2003)
  • [156] AN Kirillov, M Shimozono, A generalization of the Kostka–Foulkes polynomials, Journal of Algebraic Combinatorics, 15, 27-69 (2002)
  • [157] AN Kirillov, M Taneda, Generalized Umemura Polynomials and the Hirota-Miwa Equation, MathPhys Odyssey 2001: Integrable Models and Beyond In Honor of Barry M (2002)
  • [158] AN Kirillov, Introduction to tropical combinatorics, combinatorics, 82-150 (2001)
  • [159] AN Kirillov, Combinatorics of Young tableaux and configurations, Proceedings of the St. Petersburg Mathematical Society, 7, 17-98 (2001)
  • [160] JF Van Diejen, AN Kirillov, Determinantal formulas for zonal spherical functions on hyperboloids, Mathematische Annalen, 319(2), 215-234 (2001)
  • [161] AN Kirillov, N Liskova, Physics And Combinatorics, Procs Of The Nagoya 2000 Intl Workshop, World Scientific (2001)
  • [162] AN Kirillov, A Schilling, M Shimozono, Various representations of the generalized Kostka polynomials, The Andrews Festschrift: Seventeen Papers on Classical Number Theory and … (2001)
  • [163] AN Kirillov, N Liskova, Bethe's states for generalized XXX and XXZ models, Physics and Combinatorics, 151-163 (2001)
  • [164] AN Kirillov, A Tsuchiya, H Umemura, Physics And Combinatorics, Procs Of Nagoya 1999 Intl Wkshp, World Scientific (2001)
  • [165] A Tsuchiya, AN Kirillov, H Umemura, Physics and Combinatorics 1999: Procceedings [ie Proceedings] of the Nagoya 1999 International Workshop, Graduate School of Mathematics, Nagoya University, World Scientific (2001)
  • [166] AN Kirillov, New combinatorial formula for modified Hall-Littlewood polynomials, Contemporary Mathematics, 254, 283-334 (2000)
  • [167] AN Kirillov, T Maeno, Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa–Intriligator formula, Discrete Mathematics 217 (1-3), 191-223 (2000)
  • [168] AN Kirillov, On Some Quadratic Algebras: Jucys—Murphy and Dunkl Elements, Calogero—Moser—Sutherland Models, 231-248 (2000)
  • [169] AN Kirillov, On some quadratic algebras, American Mathematical Society-Series 2, 201, 91-114 (2000)
  • [170] AN Kirillov, Generalization of the Gale–Ryser Theorem, European Journal of Combinatorics, 21(8), 1047-1055 (2000)
  • [171] AD Berenstein, AN Kirillov, Domino tableaux, Schützenberger involution and action of the symmetric group, Discrete Math 225 (1-3), 5-24 (2000)
  • [172] G Hatayama, AN Kirillov, A Kuniba, M Okado, T Takagi, Y Yamada, Character formulae of ̂sln-modules and inhomogeneous paths, Nuclear Physics B, 536(3), 575-616 (1998)
  • [173] AN Kirillov, A Kuniba, T Nakanishi, Skew Young diagram method in spectral decomposition of integrable lattice models II: Higher levels, Nuclear Physics B, 529(3), 611-638 (1998)
  • [174] AN Kirillov, t-deformation of quantum Schubert polynomials, arXiv preprint math/9802001 (1998)
  • [175] AN Kirillov, Combinatorial Formula for Modified Hall-Littlewood Polynomials (1998)
  • [176] AN Kirillov, A Kuniba, T Nakanishi, Skew Young diagram method in spectral decomposition of integrable lattice models, Communications in Mathematical Physics, 185(2), 441-465 (1997)
  • [177] AN Kirillov, NA Liskova, Completeness of Bethe's states for the generalized XXZ model, Journal of Physics A: Mathematical and General, 30(4) (1997)
  • [178] S Fomin, AN Kirillov, The Yang-Baxter equation, symmetric functions, and Schubert polynomials, Discrete Mathematics 153 (1-3), 123-143 (1996)
  • [179] S Fomin, A Kirillov, Combinatorial 𝐵_ {𝑛}-analogues of Schubert polynomials, Transactions of the American Mathematical Society, 348(9), 3591-3620 (1996)
  • [180] AN Kirillov, M Noumi, $q$-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients, q-alg (1996)
  • [181] AN Kirillov, NA Liskova, Completeness of Bethe's states for generalized $ XXZ $ model, II, arXiv preprint hep-th/9607012 (1996)
  • [182] AN Kirillov, A Lascoux, B Leclerc, JY Thibon, Séries génératrices pour les tableaux de dominos, Comptes rendus de l'Académie des sciences. Série 1, Mathématique, 318(5) (1994)
  • [183] AN Kirillov, A Lascoux, B Leclerc, JY THIBON, Generating series for domino tableaux, COMPTES RENDUS DE L'ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 318(5), 395-400 (1994)
  • [184] L Bégin, AN Kirillov, P Mathieu, MA Walton, Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules, letters in mathematical physics, 28(4), 257-268 (1993)
  • [185] AN Kirillov, P Mathieu, D Sénéchal, MA Walton, Can fusion coefficients be calculated from the depth rule?, Nuclear Physics B, 391(3), 651-674 (1993)
  • [186] S Fomin, AN Kirillov, Yang-Baxter equation, symmetric functions and Grothendieck polynomials, arXiv preprint hep-th/9306005 (1993)
  • [187] AN Kirillov, Dilogarithm identities, partitions and spectra in conformal field theory, I, arXiv preprint hep-th/9212150 (1992)
  • [188] AN Kirillov, DECOMPOSITION OF SYMMETRIC AND EXTERIOR POWERS OF THE ADJOINT REPRESENTATION OF${\mathfrak g}l_N$1: UNIMODALITY OF PRINCIPAL SPECIALIZATION …, International Journal of Modern Physics A, 7(supp01b), 545-579 (1992)
  • [189] AN Kirillov, P Mathieu, D Senechal, MA Walton, Crystallising the depth rule for WZNW fusion coefficients, arXiv preprint hep-th/9209114 (1992)
  • [190] NA Liskova, AN Kirillov, Clebch-Gordan and Racah-Wigner coefficients for$U_q(SU(1,1))$, International Journal of Modern Physics A, 7(supp01b), 611-621 (1992)
  • [191] AN Kirillov, Fusion algebra and Verlinde's formula, arXiv preprint hep-th/9212084 (1992)
  • [192] LC Biedenharn, E Celeghini, VG Drinfeld, LD Faddeev, VS Retakh et al., First workshop" Quantum Groups, Deformation Theory and Representation Theory"(15-28 October 1990), Quantum Groups: Proceedings of Workshops Held in the Euler International … (1992)
  • [193] AN Kirillov, Decomposition of Symmetric and Exterior Powers of the Adjoint Representation of, Research Institute for Mathematical Sciences (1991)
  • [194] AN Kirillov, Decomposition of Symmetric and Exterior Powers of the Adjoint Representation of GlN., Kyoto University, Research Institute for Mathematical Sciences (1991)
  • [195] 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)
  • [196] AN Kirillov, VE Korepin, The resonating valence bond in quasicrystals, Leningrad Math. J, 1, 343-377 (1990)
  • [197] AN Kirillov, Identities for the Rogers dilogarithm function connected with simple Lie algebras, Journal of Soviet Mathematics, 47, 2450-2459 (1989)
  • [198] AN Kirillov, T-invariance, CPT-invariance, and local commutativity for the quantum (cosh ϕ)-model, Journal of Soviet Mathematics, 40, 6-13 (1988)
  • [199] 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)
  • [200] AN Kirillov, NY Reshetikhin, Exact solution of the Heisenberg XXZ model of spin s, Journal of Soviet Mathematics, 35, 2627-2643 (1986)
  • [201] AN Kirillov, Combinatorial identities, and completeness of eigenstates of the Heisenberg magnet, Journal of Soviet Mathematics, 30, 2298-2310 (1985)
  • [202] S Tanaka, H Katsura, N aoki Kawashima, AN Kirillov, VE Korepin, Entanglement Entropy in Valence-Bond-Solid States on Symmetric Graphs
  • [203] AN Kirillov, Universal Dunkl operators: Algebra, Combinatorics, Graph Theory, Integrable Systems and LDT
  • [204] S FOMIN, AN KIRILLOV, COMBINATORIAL Bn-ANALOGUES
  • [205] AN Kirillov, Physics and combinatorics, 1999: proceedings of the Nagoya 1999 International Workshop
  • [206] AN Kirillov, T Maeno, Exterior differential algebras and at connections on Weyl groups
  • [207] AN Kirillov, N Liskova, Physics and combinatorics, 2000: proceedings of the Nagoya 2000 International Workshop
  • [208] AN Kirillov, M Shimozono, JOURNAL OF ALGEBRAIC COMBINATORICS
  • [209] AN Kirillov, T Maeno, Braided differential calculus and quantum Schubert calculus
  • [210] NA LISKOVA, AN KIRILLOV, CLEBSCH-GORDAN AND RACAH-WIGNER
  • [211] AN Kirillov, T Maeno, algebra of complex reflection groups

 

Update Time: 2025-08-12 17:00:05