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
  • - 1986      LOMI, Lenenfrad      Doctor
  • - 1988      LOMI, Lenengrad      Doctor      Hb.D

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 (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, Journal of Modern Physics, A: Math.Theor., 49(204002), None (2016)
  • [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, None, None(None), None (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, Moscow Mathematical Journal, 15(2), 1-16 (2015)
  • [12] A. Kirillov, R. Sakamoto, Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations, J. Phys. A: Math. Theor., 47(205207 (20pp)), None (2014)
  • [13] A. Isaev, A. Kirillov, Bethe subalgebras in Hecke algebra and Gaudin models, Letters in Mathematical Physics, 104(None), 179-193 (2013)
  • [14] A. Kirillov, On some algebraic and combinatorial properties of Dunkl elements, International Journal of Modern Physics B, 26(27n28), None (2013)
  • [15] A. Kirillov, On some combinatorial and algebraic properties of Dunkl elements RIMS Kokyuroku, 1795, 1-44, Kyoto University, 2012
  • [16] A. Kirillov, On some algebraic and combinatorial properties of Dunkl elements, International Journal of Modern Physics B, 26 (2012), No. 27n28
  • [17] A. Kirillov, T. Maeno, Affine nil-Hecke algebras and braided differential structure on affine Weyl groups, Publ. RIMS, 48(None), 215-228 (2012)
  • [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, Paths and Kostka-Macdonald polynomials, Moscow Math. Journal, 9(2009), 823-854 (2009)
  • [21] A. Kirillov, R. Sakamoto, Relationships between two approaches: rigged configurations and 10-eliminations, Lett. Math. Phys., 89(2009), 51-65 (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, Int. Math. Res. Not. IMRN, None(no.14), 23pp (2008)
  • [24] Feigin B., A. Kirillov, Loktev S., Combinatorics and geometry of higher level Weyl modules, Moscow Seminar on Mathematical Physics II, 221(None), 33-47 (2005)
  • [25] 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
  • [26] 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
  • [27] A. Kirillov, T.Maeno, Exterior differential algebras and flat connections on Weyl groups, Proceedings of the Japan Academy, 81(30-35), 2004, 9p. (2005)
  • [28] 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
  • [29] A. Kirillov, An invitation to the generalized saturation conjecture, Publications of RIMS Kyoto University, 40(None), 1147-1239 (2004)
  • [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, Rocky Mountain Journal of Mathematics, 32(2), 10 (2002)
  • [33] A. Kirillov, M.Taneda, Generalized Umemura polynomials and the Hirota-Miwa equations, MathPhys Odyssey 2001: Integrable Models and Beyond, 23(None), 313-332 (2002)
  • [34] A. Kirillov,A.Schilling,M.Shimozono, A bijection between Littlewood-Richardson tableaux and rigged configurations, Selecta Mathematica, 8(None), 67-135 (2002)
  • [35] A. Kirillov, M.Shimozono, A generalization of the Kostka-Foulkes polynomials, Journal of Algebraic Combinatorics, 15(2002), 27-69 (2002)
  • [36] A. Kirillov, Cauchy identities for universal Schubert polynomials, Zap. Nauch. Sem. POMI, 283(None), 123-139 (2001)
  • [37] 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
  • [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. 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
  • [43] A.Kirillov, Some remarkable quadratic algebras and Schubert Calculus, Proceedings of the 45-th Symposium on Algebra, 45(8), 142-151 (2000)
  • [44] A.Berenstein, A.Kirillov, Domino tableaux, Schutzenberger involution, and the symmetric group action, Discrete Mathematics, 225(1), 15-24 (2000)
  • [45] A.Kirillov, Generalization of the Gale-Ryser theorem, European Journal of Combinatorics, 21(4), 1047-1055 (2000)
  • [46] 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
  • [47] 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, null(301-312), None (2000)
  • [48] J.F. van Diejen, A.Kirillov, Formulas for q-spherical functions using inverse scattering theory of reflectionless Jacobi operators, Comm. Math. Phys., 210(2), 335-369 (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, None(None), 231-248 (2000)
  • [50] J.F. van Diejen, A.Kirillov, A combinatorial formula for the associated Legendre functions of integer degree, Advances in Mathematics, 149(2000), 61-88 (2000)
  • [51] A.Kirillov, t-Deformations of quantum Schubert polynomials, Funkcialaj Ekvacioj, 43(null), 57-69 (2000)
  • [52] A.Kirillov, A.Tsuchiya, H.Umemura, A remark on the Harish-Chandra series for hyperboloids, Physics and Combinatorics 1999 (Proceedings of the Nagoya 1999 International Workshop on Physics and Combinatorics, Nagoya University, August 23-27, 1999), None(None), 11-15 (1999)
  • [53] A.Kirillov, A.Tsuchiya, H.Umemur, Ubiquity of Kostka polynomials, Physics and Combinatorics 1999 (Proceedings of the Nagoya 1999 International Workshop on Physics and Combinatorics, Nagoya University, August 23-27, 1999), None(None), 85-200 (1999)
  • [54] A.Kirillov, Quantum Schubert polynomials and quantum Schur functions, Intern. Journ. of Algebra and Computation, 9(2), 385-404 (1999)
  • [55] 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(None), 227-243 (1999)
  • [56] 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, None(None), 266-274 (1999)
  • [57] 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
  • [58] 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
  • [59] S.Fomin, A.Kirillov, Quadratic algebras, Dunkl elements, and Schubert calculus, Advances in Geometry, 147(182), None (1998)
  • [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] A.Kirillov, M.Noumi, Affine Hecke algebras and raising operators for Macdonald polynomials, Duke Math. Journ., 93(1), 1-41 (1998)
  • [63] 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
  • [64] 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.
  • [65] 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
  • [66] 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
  • [67] S.Fomin, A.Kirillov, Reduced words and plane partitions, Journal of Algebraic Combinatorics, 6(2), 311-319 (1997)
  • [68] A.Kirillov, Quantum Grothendieck polynomials, Algebraic Methods and q-Special Functions (Montreal, PQ, May 13-17, 1996), CRM Proc. Lecture Notes 22(None), 215-226 (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] S.Fomin, A.Kirillov, Universal exponential solution of the Yang-Baxter equation, Lett. in Math. Phys., 37(1), 273-284 (1996)
  • [72] A.Kirillov, Dilogarithm identities, Lectures in Mathematical Sciences the University of Tokyo, 7(1995), 96p. (1996)
  • [73] 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)
  • [74] A.Kirillov, Dilogarithm identities, Lectures in Mathematical Sciences the University of Tokyo, 7 (1995), 96p.
  • [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] S.Fomin, A.Kirillov, Grothendieck polynomials and the Yang-Baxter equation, Proceedings of the 6th International Conference on Formal Power Series and Algebraic Combinatorics, DIMACS, 1994(183-190), None (1994)
  • [77] A.Kirillov, Dilogarithm identities, partitions and spectra in conformal field theory, Part I, Algebra i Analiz 6 (1994), no.2, 152-175.
  • [78] 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
  • [79] 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.
  • [80] 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, null(215-230), None (1993)
  • [81] 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)
  • [82] A.Kirillov, Dilogarithm identities and spectra in conformal field theory, Low-dimensional Topology and Quantum Field Theory, None(Cambridge, 1992), 99-108 (1993)
  • [83] 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, None(None), None (1992)
  • [84] A.Kirillov, Unimodality of generalized Gaussian coefficients, C.R. Acad. Sci. Paris Ser. I, 315(5), 497-501 (1992)
  • [85] S.V.Kerov, A.Kirillov, Combinatorics of rational representations of the group GL(n,C), None, 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, Zap. Nauch. Sem. LOMI, 168(1988), 67-84, 264-276 (1991)
  • [90] A.Kirillov, On some properties of the Robinson-Schensted correspondence, Proceedings of Hayashibara conference on special functions, None(None), 122-126 (1990)
  • [91] A.Kirillov, Representation of quantum groups, combinatorics, q-orthogonal polynomials and link invariants (Russian), None, None(None), 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), None (1987)
  • [111] A.Kirillov, N.Yu.Reshetikhin, Quantum inhomogeneous XXZ magnet and non-linear $sigma$-models, Proceedings of Paris-Meudon Colloquium, Paris, 1987, None(None), 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, Lett. in Math. Phys., 12(1986), 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, None(None), 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), None (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, None(1977), 76 (1977)

 

Update Time: 2025-02-26 16:37:16