Publications by Anatol N. Kirillov


  1. Bethe subalgebras in Hecke algebra and Gaudin models (with A.Isaev) Letters in Mathematical Physics, 104, (2014) 179-193
    Preprint RIMS-1775, 2013

  2. On some combinatorial and algebraic properties of Dunkl elements RIMS Kokyuroku, 1795, 1-44, Kyoto University, 2012

  3. On some algebraic and combinatorial properties of Dunkl elements
    The Korepin Festschrift, World Scientific (2013), 171-198

  4. On some algebraic and combinatorial properties of Dunkl elements
    International Journal of Modern Physics B, 26 (2012), No. 27n28

  5. Affine nil-Hecke algebras and braided differential structure on affine Weyl groups (with T.Maeno)
    Publ. RIMS, no. 48 (2012), 215-228

  6. Entanglment in valence-bond-solid states on symmetric graphs (with H.Katsura, N.Kawashima, V.Korepin, S.Tanaka)
    J. Phys. A 43 (2010), no.255303, 28p.

  7. Nichols-Woronowicz model of coinvariant algebra of complex reflection groups (with T.Maeno)
    J. Pure Appl. Algebra 214 (2010), 402-409

  8. Paths and Kostka-Macdonald polynomials (with R.Sakamoto)
    Moscow Math. Journal 9 (2009), 823-854

  9. Relationships between two approaches: rigged configurations and 10-eliminations (with R.Sakamoto)
    Lett. Math. Phys. 89 (2009), 51-65

  10. Braided differential structure on Weyl groups, quadratic algebras, and elliptic functions (with T.Maeno)
    Int. Math. Res. Not. IMRN no.14 (2008), 23pp

  11. Combinatorics and geometry of higher level Weyl modules
    Moscow Seminar on Mathematical Physics II, Amer. Math. Soc. Transl. Ser. 2, 221, Amer. Math. Soc., Providence, RI, 2007, 33-47 (with Feigin B., A.N. Loktev)
    Preprint RIMS-1495, 2005, 15p.
    math.QA/0503315

  12. 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

  13. Wonderful Amoebas (Japanese, with T.Maeno)
    Sugaku 58 (2006), 151-164, translation in Sugaku Expositions 22 (2009), 107-120

  14. On some noncommutative algebras related with K-theory of flag varieties, I (with T.Maeno)
    IRMN 60 (2005), 3753-3789
    Preprint RIMS, 2005, 25p.
    math.CO/0504290

  15. A note on quantization on Nichols algebra model for Schubert calculus on Weyl groups (with T.Maeno)
    Lett. in Math. Phys. 72 (2005) 233-241
    Preprint RIMS-1481, 2004, 8p.
    math.QA/0412069

  16. Hypergeometric generating function of L-function, Slater's identities and Quantum invariant (with K.Hikami)
    Algebra i Analiz 17 (2005), no.1, 190-208
    Preprint RIMS-1463, 2004, 18p.
    math-ph/0406042

  17. Exterior differential algebras and flat connections on Weyl groups (with T.Maeno)
    Proceedings of the Japan Academy 81 (2005), 30-35
    Preprint RIMS-1469, 2004, 9p.
    math.QA/0407291

  18. An invitation to the generalized saturation conjecture
    Publications of RIMS Kyoto University 40 (2004), 1147-1239
    Preprint RIMS-1452, 2004, 69p.
    math.CO/0404353

  19. Noncommutative algebras related with Schubert calculus on Coxeter groups (with T.Maeno)
    European Journal of Combinatorics, 25 (2004), 1301-1325
    Preprint RIMS-1437, 2003, 23p.
    math.CO/0310068

  20. Torus knot and minimal model (with K.Hikami)
    Physics Letters B 575 (2003), 343-348
    hep-th/0308152, 2003, 10p.

  21. Generalized Umemura polynomials (with M.Taneda)
    Rocky Mountain Journal of Mathematics 32 (2002), no. 2,
    math.CO/0010279, 2000, 10p.

  22. Generalized Umemura polynomials and the Hirota-Miwa equations (with M.Taneda)
    MathPhys Odyssey 2001: Integrable Models and Beyond, in honor of Barry M. McCoy (ed. M.Kashiwara and T.Miwa), 313-332,
    Progress in Mathematical Physics 23, Birkhauser, Boston, 2002
    math.CO/0106025, 2001, 19p.

  23. A bijection between Littlewood-Richardson tableaux and rigged configurations (with A.Schilling and M.Shimozono)
    Selecta Mathematica 8 (2002), 67-135
    Preprint Hokkaido University # 441, 1999, 66p.
    math.QA/9901037

  24. A generalization of the Kostka-Foulkes polynomials (with M.Shimozono)
    Journal of Algebraic Combinatorics 15 (2002), 27-69
    math.QA/9803062, 1998, 37p.

  25. Cauchy identities for universal Schubert polynomials
    Zap. Nauch. Sem. POMI 283 (2001), 123-139
    q-alg/9703047, 1997, 16p.

  26. 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

  27. Bethe's states for generalized XXX and XXZ models (with N.A. Liskova)
    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

  28. A remark on the Harish-Chandra series for hyperboloids (with J.F. van Diejen)
    Physics and Combinatorics 1999 (Proceedings of the Nagoya 1999 International Workshop on Physics and Combinatorics, Nagoya University, August 23-27, 1999, ed. A.Kirillov, A.Tsuchiya and H.Umemura), 11-15,
    World Scientific, Singapore, 2001

  29. 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, ed. A.Kirillov, A.Tsuchiya and H.Umemur), 85-200,
    World Scientific, Singapore, 2001
    math.QA/9912094

  30. Some remarkable quadratic algebras and Schubert Calculus
    Proceedings of the 45-th Symposium on Algebra, Kyushu University, August 7-10, 2000, 142-151

  31. Determinantal formulas for zonal spherical functions of hyperboloids (with J.F. van Diejen)
    Mathematische Annalen 319 (2001), no.2, 215-234

  32. Domino tableaux, Schutzenberger involution, and the symmetric group action (with A.Berenstein)
    Discrete Mathematics, 225 (2000), 15-24

  33. Generalization of the Gale-Ryser theorem
    European Journal of Combinatorics, 21 (2000), 1047-1055
    hep-th/9304099

  34. 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

  35. 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

  36. 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

  37. Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula (with T.Maeno)
    Discrete Mathematics 217 (2000), 191-224
    q-alg/9610022

  38. Formulas for q-spherical functions using inverse scattering theory of reflectionless Jacobi operators (with J.F. van Diejen)
    Comm. Math. Phys. 210 (2000), 335-369

  39. 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

  40. On some quadratic algebras: Jucys-Marphy and Dunkl elements
    Calogero-Moser-Sutherland models, (Montreal, PQ, March 10-15, 1997) CRM Series in Mathematical Physics, Springer, New York, 2000, 231-248

  41. A combinatorial formula for the associated Legendre functions of integer degree (with J.F. van Diejen)
    Advances in Mathematics 149 (2000), 61-88

  42. t-Deformations of quantum Schubert polynomials
    Funkcialaj Ekvacioj 43 (2000), 57-69
    math.QA/9802001

  43. Quantum Schubert polynomials and quantum Schur functions
    Intern. Journ. of Algebra and Computation 9 (1999), 385-404
    q-alg/9701005

  44. Quantum Grothendieck polynomials
    Algebraic Methods and q-Special Functions (Montreal, PQ, May 13-17, 1996)
    CRM Proc. Lecture Notes 22, Amer. Math. Soc., 1999, 215-226
    q-alg/9610034

  45. q-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients (with M.Noumi)
    Algebraic Methods and q-Special Functions (Montreal, PQ, May 13-17, 1996)
    CRM Proc. Lecture Notes 22, Amer. Math. Soc., 1999, 227-243
    q-alg/9605005

  46. On a bijection between Littlewood-Richardson tableaux and rigged configurations (with A.Schilling and M.Shimozono)
    Proceedings of the 11th International Conference on Formal Power Series and Algebraic Combinatorics, Barcelona, June 7-11, 1999, 266-274.

  47. Various representations of the generalized Kostka polynomials (with A.Schilling and M.Shimozono)
    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.

  48. Character formulae of sl_n modules and inhomogeneous paths (with G.Hatayama, A.Kuniba, M.Okado, T.Takagi and Y.Yamada)
    Nucl. Phys. B 536 (1999), 575-616
    math.QA/9802085

  49. Quadratic algebras, Dunkl elements, and Schubert calculus (with S.Fomin)
    Advances in Geometry, 147-182, Progress in Mathematics 172, Birkhauser, Boston, 1998

  50. Skew Young diagram method in spectral decomposition of integrable lattice models II, Higher levels (with A.Kuniba and T.Nakanishi)
    Nucl. Phys. B 529 (1998), 611-638
    q-alg/9711009

  51. Domino tableaux, Schutzenberger involution and action of the symmetric group (with A.Berenstein)
    Proceedings of the 10th International Conference on Formal Power Series and Algebraic Combinatorics, Fields Institute, Toronto, 1998, 55-66.
    q-alg/9709010

  52. Affine Hecke algebras and raising operators for Macdonald polynomials (with M.Noumi)
    Duke Math. Journ. 93 (1998), no.1, 1-41.
    q-alg/9605004

  53. Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula (with T.Maeno)
    Proceedings of the 9th International Conference on Formal Power Series and Algebraic Combinatorics, Wien, July 14-July 18, 1997, 301-312.

  54. Skew Young diagram method in spectral decomposition of integrable lattice models
    (with A.Kuniba and T.Nakanishi)
    Comm. Math. Phys. 185 (1997), no.2, 441-465.
    q-alg/9607027

  55. Completeness of Bethe's states for generalized XXZ model (with N.A.Liskova)
    J. Phys. A 30 (1997), no.4, 1209-1226.
    hepth/9407107

  56. Reduced words and plane partitions (with S.Fomin)
    Journal of Algebraic Combinatorics 6 (1997), 311-319.

  57. Combinatorial $B_n$-analogues of Schubert polynomials (with S.Fomin)
    Transactions of the AMS 348 (1996), 3591-3620.

  58. The Yang-Baxter equation, symmetric functions, and Schubert polynomials (with S.Fomin)
    Discrete Mathematics 153 (1996), 123-143.

  59. Universal exponential solution of the Yang-Baxter equation (with S.Fomin)
    Lett. in Math. Phys. 37 (1996), 273-284.

  60. Dilogarithm identities
    Progress of Theor. Phys. Suppl. 118 (1995), 61-142.

  61. Dilogarithm identities
    Lectures in Mathematical Sciences the University of Tokyo, 7 (1995), 96p.

  62. Group generated by involutions, Gelfand-Tsetlin patterns and combinatorics of Young tableaux (with A.Berenstein)
    Algebra i Analiz 7 (1995), no.1, 92-152, translation in St.Petersburg Math. J. 7 (1996), no.1, 77-127.

  63. Séries génératrices pour les tableaux de dominos (French, with A.Lascoux, B.Leclerc and J.-Y.Thibon)
    C.R. Acad. Sci. Paris Ser. I 318 (1994), no.5, 395-400.

  64. Grothendieck polynomials and the Yang-Baxter equation (with S.Fomin)
    Proceedings of the 6th International Conference on Formal Power Series and Algebraic Combinatorics, DIMACS, 1994, 183-190.

  65. Dilogarithm identities, partitions and spectra in conformal field theory, Part I
    Algebra i Analiz 6 (1994), no.2, 152-175.

  66. Formulae for the multiplicites of the occurrence of irreducible components in the tensor product of representations of simple Lie algebras (Russian, with N.Yu.Reshetikhin)
    Zap. Nauch. Sem. LOMI 205 (1993), 30-37, translation in Journal of Mathematical Sciences 80, no.3 (1996), 1768-1772

  67. Berenstein-Zelevinski triangles, elementary couplings and fusion rules
    (with P.Mathieu, L.Bégin, M.A.Walton)
    Lett. in Math. Phys. 28 (1993), no.4, 257-268.

  68. The Yang-Baxter equation, symmetric functions and Schubert polynomials (with S.Fomin)
    Proceedings of the 5th International Conference on Formal Power Series and Algebraic Combinatorics, Firenze, June 21-25, 1993, 215-230.

  69. Can fusion coefficients be calculated from the depth rule ? (with P.Mathieu, D.Sénéchal, M.A.Walton)
    Nucl. Phys. B 391 (1993), no.3, 651-674.

  70. Dilogarithm identities and spectra in conformal field theory
    Low-dimensional Topology and Quantum Field Theory (Cambridge, 1992) 99-108, NATO Adv. Sci. Inst. Ser. B Phys., 315, Plenum, New York, 1993.

  71. Crystallizing the depth rule for WZNW fusion coefficients (with P.Mathieu, D.Sénéchal, M.A.Walton)
    Proceedings of the XIXth International Colloquium on Group Theoretical Physics, Salamanca, Spain, 1992.

  72. Unimodality of generalized Gaussian coefficients
    C.R. Acad. Sci. Paris Ser. I 315 (1992), no.5, 497-501.

  73. Combinatorics of rational representations of the group GL(n,C) (Russian, with S.V.Kerov)
    Zap. Nauch. Sem. LOMI 200 (1992), 83-93, translation in Journal of Mathematical Sciences 77, no.3 (1995), 3190-3194

  74. Clebsch-Gordan and Racah-Wigner coefficients for $U_q(SU(1,1))$ (with N.A.Liskova)
    Int. Jour. Mod. Phys. A 7 (1992), 611-621.

  75. 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 (1992), 545-579.

  76. On some properties of the Robinson-Schensted correspondence
    Proceedings of Hayashibara conference on special functions, 1990, 122-126.

  77. Representation of quantum groups, combinatorics, q-orthogonal polynomials and link invariants (Russian)
    Second Ph.D thesises, LOMI, Leningrad, 1990, 300p.

  78. q-Weyl group and a multiplicative formula for universal R-matrices (with N.Yu.Reshetikhin)
    Comm. Math. Phys. 134 (1990), 316-325.

  79. The resonating valence bond in quasicristals (Russian, with V.E.Korepin)
    Algebra i Analiz 1 (1989), 47-76, translation in Leningrad Math. J. 1 (1990), n.2, 343-377.

  80. The Lagrange identity and the hook formula (Russian)
    Zap. Nauch. Sem. LOMI 172 (1989), 78-87, translation in Journal of Soviet Math. 59 (1992), 1078-1084.

  81. Representations of the algebra $U_q(sl(2))$, q-orthogonal polynomials and invariants of links (with N.Yu.Reshetikhin)
    Adv. Series in Math. Phys. 7 (1989), 285-339.

  82. On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers
    Journ. Geom. and Phys. 5 (1988), 365-389.

  83. Multiplicity of weight in irreducible tensor representations of a complete linear syperalgebra (Russian, with N.Yu.Reshetikhin)
    Funct. Anal. and Applicat. 22 (1988), no.4, 84-85.

  84. Form-factors in O(3) nonlinear $\sigma$-model (with F.A.Smirnov)
    Int. Jour. Mod. Phys. A 3 (1988), no.3, 731-741.

  85. Clebsch-Gordan quantum coefficients (Russian)
    Zap. Nauch. Sem. LOMI 168 (1988), 67-84, translation in Journal of Soviet Math. 53 (1991), 264-276.

  86. 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.

  87. Formulas for formfactors in the quantum sinh-Gordon model (Russian)
    Zap. Nauch. Sem. LOMI 164 (1987), 54-66, translation in Journal of Soviet Math. 47 (1989), 2403-2412.

  88. Solution of some combinatorial problems arising in the calculation of correlators in exactly solvable models (Russian, with F.A.Smirnov)
    Zap. Nauch. Sem. LOMI 164 (1987), 67-79, translation in Journal of Soviet Math. 47 (1989), 2413-2422.

  89. Formfactors in the SU(2)-invariant Thirring model (Russian, with F.A.Smirnov)
    Zap. Nauch. Sem. LOMI 164 (1987), 80-120, translation in Journal of Soviet Math. 47 (1989), 2423-2449.

  90. A representation of the current algebra connected with SU(2)-invariant Thirring model
    (with F.A.Smirnov)
    Phys. Lett. B 198 (1987), no.4, 506-510.

  91. The Bethe ansatz and the combinatorics of Young tableaux (Russian)
    Ph.D thesises, LOMI, Leningrad, 1987, 210p.

  92. Exact solution of the integrable XXZ Heisenberg model with arbitrary spin, I
    (with N.Yu.Reshetikhin)
    J. Phys. A 20 (1987), 1565-1586.

  93. Exact solution of the integrable XXZ Heisenberg model with arbitrary spin, II
    (with N.Yu.Reshetikhin)
    J. Phys. A 20 (1987), 1587-1597.

  94. Quantum inhomogeneous XXZ magnet and non-linear $\sigma$-models (with N.Yu.Reshetikhin)
    Proceedings of Paris-Meudon Colloquium, Paris, 1987, 235-257.

  95. Representation of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras (Russian, with N.Yu.Reshetikhin)
    Zap. Nauch. Sem. LOMI 160 (1987), 211-221, translation in Journal of Soviet Math. 52 (1990), 3156-3164.

  96. Some generalization of the Abjankar-Moh theorem (Russisn)
    Proceedings of Algebraic Conference, L'vov, 1987, part 1, p.131.

  97. The Yangians, Bethe ansatz and combinatorics (with N.Yu.Reshetikhin)
    Lett. in Math. Phys. 12 (1986), 199-208.

  98. Combinatorics, the Bethe ansatz and representations of the symmetric group (Russian, with S.V.Kerov and N.Yu.Reshetikhin)
    Zap. Nauch. Sem. LOMI 155 (1986), 50-64, translation in Journal of Soviet Math. 41 (1988), 916-924.

  99. The Bethe ansatz and the combinatorics of Young tableaux (Russian, with N.Yu.Reshetikhin)
    Zap. Nauch. Sem. LOMI 155 (1986), 65-115, translation in Journal of Soviet Math. 41 (1988), 925-955.

  100. T-invariance, CPT-invariants and local commutativity of the quantum $(ch\varphi)_2$ model (Russian)
    Zap. Nauch. Sem. LOMI 146 (1985), 9-19, translation in Journal of Soviet Math. 40 (1988), 6-12.

  101. Norms of bound states (Russian, with V.E.Korepin)
    Zap. Nauch. Sem. LOMI 146 (1985), 20-30, translation in Journal of Soviet Math. 40 (1988), 13-21.

  102. Classification of the string solutions of Bethe equations in the XXZ-model of arbitrary spin (Russian, with N.Yu.Reshetikhin)
    Zap. Nauch. Sem. LOMI 146 (1985), 31-46, translation in Journal of Soviet Math. 40 (1988), 22-34.

  103. Properties of kernels of integral equations in the XXZ-model of arbitrary spin
    (Russian, with N.Yu.Reshetikhin)
    Zap. Nauch. Sem. LOMI 146 (1985), 47-91, translation in Journal of Soviet Math. 40 (1988), 35-71.

  104. Exact solution of XXZ-Heisenberg model of the higher spin (Russian)
    Zap. Nauch. Sem. LOMI 145 (1985), 109-133, translation in Journal of Soviet Math. 35 (1986), 2627-2643.

  105. Completeness of states of the generalized Heisenberg magnet (Russian)
    Zap. Nauch. Sem. LOMI 134 (1985), 169-189, translation in Journal of Soviet Math. 36 (1987), 115-128.

  106. Norm pairing in a two-dimensional local field (Russian, with S.V.Vostokov)
    Zap. Nauch. Sem. LOMI 132 (1983), 76-84, translation in Journal of Soviet Math. 30 (1985), 1847-1853.

  107. 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.

  108. Mixed Hodge structure of the isolated singularity of the hypersuface
    Shot Communications, ICM-82, Warszawa, 1982, sec.6, p.34.

  109. Milnor's number of isolated singularity of complete intersection (Russian)
    Proceedings of Algebraic conference, Leningrad, 1981, part 1, p.97.

  110. 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.

  111. 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.

  112. Convex polytops and formal groups (Russian)
    Zap. Nauch. Sem. LOMI 75 (1978), 87-90, translation in Journal of Soviet Math. 37 (1987), 974-976.

  113. Classification of the formal O-modules (Russian)
    Proceedings of Algebraic conference, Krasnoyarsk, 1977, p.76.

  114. Commutative formal groups (Russian)
    Zap. Nauch. Sem. LOMI 57 (1976), 117-124, translation in Journal of Soviet Math. 11 (1979), 613-619.

  115. Lutz filtration of formal groups (Russian, with M.I.Bashmakov)
    Izv. Acad. of Scien. USSR 139 (1975), no.6, 1227-1239.


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