Анзац Бете и комбинаторика таблиц Юнга
А. Н. Кириллов, Н. Ю. Решетихин

Эта публикация цитируется в следующих статьяx:

1. Matteo Mucciconi, Makiko Sasada, Tomohiro Sasamoto, Hayate Suda, “Relationships between two linearizations of the box-ball system: Kerov–Kirillov–Reschetikhin bijection and slot configuration”, Forum of Mathematics, Sigma, 12 (2024)  
2. Naihuan Jing, Ning Liu, “A multiparametric Murnaghan-Nakayama rule for Macdonald polynomials”, Journal of Combinatorial Theory, Series A, 207 (2024), 105920  
3. Igor Pak, Proceedings of Symposia in Pure Mathematics, 110, Open Problems in Algebraic Combinatorics, 2024, 191  
4. Amol Aggarwal, Alexei Borodin, Leonid Petrov, Michael Wheeler, “Free fermion six vertex model: symmetric functions and random domino tilings”, Sel. Math. New Ser., 29:3 (2023)  
5. Claire R. Gilson, “A visual approach to the ultradiscrete KdV equation with non-integer site values”, Proc. R. Soc. A., 478:2262 (2022)  
6. Dmitry Chernyak, Sébastien Leurent, Dmytro Volin, “Completeness of Wronskian Bethe Equations for Rational ${\mathfrak {\mathfrak {gl}}_{{{\mathsf {m}}}|{{\mathsf {n}}}}}$ Spin Chains”, Commun. Math. Phys., 391:3 (2022), 969  
7. Michael Chmutov, Gabriel Frieden, Dongkwan Kim, Joel Brewster Lewis, Elena Yudovina, “An affine generalization of evacuation”, Sel. Math. New Ser., 28:4 (2022)  
8. Sylvie Corteel, Jim Haglund, Olya Mandelshtam, Sarah Mason, Lauren Williams, “Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials”, Sel. Math. New Ser., 28:2 (2022)  
9. Atsuo Kuniba, Grégoire Misguich, Vincent Pasquier, “Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$”, SciPost Phys., 10:4 (2021)  
10. Paweł Jakubczyk, Andrzej Wal, Michał Kaczor, Dorota Jakubczyk, Mirosław Łabuz, Jan Milewski, “A Maple package for combinatorial aspects of Bethe Ansatz”, Computer Physics Communications, 261 (2021), 107720  
11. Anatol N. Kirillov, Progress in Mathematics, 340, Representation Theory, Mathematical Physics, and Integrable Systems, 2021, 453  
12. Timothee W. Bryan, Naihuan Jing, “An iterative formula for the Kostka–Foulkes polynomials”, J Algebr Comb, 54:2 (2021), 625  
13. Katsuki Kobayashi, “Nonautonomous discrete elementary Toda orbits and their ultradiscretization”, J. Phys. A: Math. Theor., 54:45 (2021), 455203  
14. Emily Gunawan, Travis Scrimshaw, “Kirillov–Reshetikhin Crystals B1, s for $\widehat {\mathfrak {s}\mathfrak {l}}_{n}$ Using Nakajima Monomials”, Algebr Represent Theor, 23:4 (2020), 1  
15. R S Vieira, A Lima-Santos, “The algebraic Bethe Ansatz and combinatorial trees”, Journal of Integrable Systems, 4:1 (2019)  
16. Takashi Imoto, Jun Sato, Tetsuo Deguchi, “Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain”, J. Phys. A: Math. Theor., 52:3 (2019), 035203  
17. G. Banaszak, D. Blinkiewicz, P. Krasoń, J. Milewski, “Heisenberg and Bethe Field Extensions Applied to Magnetic Rings”, Acta Phys. Pol. A, 133:3 (2018), 441  
18. Ben Salisbury, Travis Scrimshaw, “Rigged configurations and the $*$-involution”, Lett Math Phys, 108:9 (2018), 1985  
19. Atsuo Kuniba, Hanbaek Lyu, Masato Okado, “Randomized box–ball systems, limit shape of rigged configurations and thermodynamic Bethe ansatz”, Nuclear Physics B, 937 (2018), 240  
20. Shiyuan LIU, “Fermionic formula for double Kostka polynomials”, J. Math. Soc. Japan, 70:1 (2018)  
21. Jin Hong, Hyeonmi Lee, “Rigged configuration descriptions of the crystals B(∞) and B(λ) for special linear Lie algebras”, Journal of Mathematical Physics, 58:10 (2017)  
22. Nick Dorey, David Tong, Carl Turner, “A matrix model for WZW”, J. High Energ. Phys., 2016:8 (2016)  
23. Per Alexandersson, “Gelfand–Tsetlin polytopes and the integer decomposition property”, European Journal of Combinatorics, 54 (2016), 1  
24. Tetsuo Deguchi, Pulak Ranjan Giri, “Exact quantum numbers of collapsed and non-collapsed two-string solutions in the spin-1/2 Heisenberg spin chain”, J. Phys. A: Math. Theor., 49:17 (2016), 174001  
25. Masato Okado, “Similarity and Kirillov-Schilling-Shimozono Bijection”, Algebr Represent Theor, 19:4 (2016), 975  
26. Pulak Ranjan Giri, Tetsuo Deguchi, “Heisenberg model and rigged configurations”, J. Stat. Mech., 2015:7 (2015), P07007  
27. Tetsuo Deguchi, Pulak Ranjan Giri, “Non self-conjugate strings, singular strings and rigged configurations in the Heisenberg model”, J. Stat. Mech., 2015:2 (2015), P02004  
28. Per Alexandersson, “A combinatorial proof of the skew K-saturation theorem”, Discrete Mathematics, 338:1 (2015), 93  
29. Pulak Ranjan Giri, Tetsuo Deguchi, “Singular eigenstates in the even(odd) length Heisenberg spin chain”, J. Phys. A: Math. Theor., 48:17 (2015), 175207  
30. Reiho Sakamoto, “Rigged configurations approach for the spin-1/2 isotropic Heisenberg model”, J. Phys. A: Math. Theor., 48:16 (2015), 165201  
31. Reiho Sakamoto, “Rigged Configurations and Kashiwara Operators”, SIGMA, 10 (2014), 028, 88 pp.      
32. Per Alexandersson, “Stretched skew Schur polynomials are recurrent”, Journal of Combinatorial Theory, Series A, 122 (2014), 1  
33. Anatol N Kirillov, Reiho Sakamoto, “Singular solutions to the Bethe ansatz equations and rigged configurations”, J. Phys. A: Math. Theor., 47:20 (2014), 205207  
34. Taichiro Takagi, “Combinatorial aspects of the conserved quantities of the tropical periodic Toda lattice”, J. Phys. A: Math. Theor., 47:39 (2014), 395201  
35. Christian Korff, “Cylindric Versions of Specialised Macdonald Functions and a Deformed Verlinde Algebra”, Commun. Math. Phys., 318:1 (2013), 173  
36. Rei Inoue, Atsuo Kuniba, Taichiro Takagi, “Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry”, J. Phys. A: Math. Theor., 45:7 (2012), 073001  
37. Masato Okado, Reiho Sakamoto, “Stable rigged configurations for quantum affine algebras of nonexceptional types”, Advances in Mathematics, 228:2 (2011), 1262  
38. Cristian Lenart, “Hall–Littlewood polynomials, alcove walks, and fillings of Young diagrams”, Discrete Mathematics, 311:4 (2011), 258  
39. Atsuo Kuniba, Tomoki Nakanishi, Junji Suzuki, “T-systems andY-systems in integrable systems”, J. Phys. A: Math. Theor., 44:10 (2011), 103001  
40. Ben Brubaker, Daniel Bump, Solomon Friedberg, “Schur Polynomials and The Yang-Baxter Equation”, Commun. Math. Phys., 308:2 (2011), 281  
41. Atsuo Kuniba, Taichiro Takagi, “Fermionic partition functions for a periodic soliton cellular automaton”, J. Phys. A: Math. Theor., 44:13 (2011), 135204  
42. Atsuo Kuniba, Taichiro Takagi, “Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for $A^{(1)}_n$”, SIGMA, 6 (2010), 013, 52 pp.      
43. Taichiro Takagi, “Level Set Structure of an Integrable Cellular Automaton”, SIGMA, 6 (2010), 027, 18 pp.      
44. Masato Okado, Reiho Sakamoto, “Combinatorial R-Matrices for Kirillov–Reshetikhin Crystals of Type D(1)n, B(1)n, A(2)2n−1”, International Mathematics Research Notices, 2010:3 (2010), 559  
45. J.-C. Novelli, J.-Y. Thibon, L.K. Williams, “Combinatorial Hopf algebras, noncommutative Hall–Littlewood functions, and permutation tableaux”, Advances in Mathematics, 224:4 (2010), 1311  
46. Anatol N. Kirillov, Reiho Sakamoto, “Paths and Kostka–Macdonald polynomials”, Mosc. Math. J., 9:4 (2009), 823–854        
47. Giovanni Feverati, Paul A Pearce, Nicholas S Witte, “Physical combinatorics and quasiparticles”, J. Stat. Mech., 2009:10 (2009), P10013  
48. R. Sakamoto, “Kirillov-Schilling-Shimozono Bijection as Energy Functions of Crystals”, International Mathematics Research Notices, 2009  
49. Taichiro Takagi, “Creation of Ballot Sequences in a Periodic Cellular Automaton”, J. Phys. Soc. Jpn., 78:2 (2009), 024003  
50. Reiho Sakamoto, “Crystal interpretation of Kerov–Kirillov–Reshetikhin bijection II. Proof for $\mathfrak{sl}_{n}$ case”, J Algebr Comb, 27:1 (2008), 55  
51. Reiho Sakamoto, “A crystal theoretic method for finding rigged configurations from paths”, J. Phys. A: Math. Theor., 41:35 (2008), 355208  
52. ATSUO KUNIBA, REIHO SAKAMOTO, “COMBINATORIAL BETHE ANSATZ AND GENERALIZED PERIODIC BOX-BALL SYSTEM”, Rev. Math. Phys., 20:05 (2008), 493  
53. Atsuo Kuniba, Reiho Sakamoto, “Combinatorial Bethe Ansatz and Ultradiscrete Riemann Theta Function with Rational Characteristics”, Lett Math Phys, 80:3 (2007), 199  
54. Atsuo Kuniba, Reiho Sakamoto, Yasuhiko Yamada, “Tau functions in combinatorial Bethe ansatz”, Nuclear Physics B, 786:3 (2007), 207  
55. Anne Schilling, Mark Shimozono, “X=M for symmetric powers”, Journal of Algebra, 295:2 (2006), 562  
56. A. Schilling, “Crystal structure on rigged configurations”, International Mathematics Research Notices, 2006  
57. Atsuo Kuniba, Akira Takenouchi, “Bethe ansatz atq= 0 and periodic box–ball systems”, J. Phys. A: Math. Gen., 39:11 (2006), 2551  
58. Anne Schilling, Philip Sternberg, “Finite-dimensional crystals B2,s for quantum affine algebras of type D(1)n”, J Algebr Comb, 23:4 (2006), 317  
59. A. Kuniba, T. Takagi, A. Takenouchi, “Bethe ansatz and inverse scattering transform in a periodic box–ball system”, Nuclear Physics B, 747:3 (2006), 354  
60. Atsuo Kuniba, Reiho Sakamoto, “The Bethe ansatz in a periodic box–ball system and the ultradiscrete Riemann theta function”, J. Stat. Mech., 2006:09 (2006), P09005  
61. Atsuo Kuniba, Masato Okado, Reiho Sakamoto, Taichiro Takagi, Yasuhiko Yamada, “Crystal interpretation of Kerov–Kirillov–Reshetikhin bijection”, Nuclear Physics B, 740:3 (2006), 299  
62. Mark Shimozono, Mike Zabrocki, “Deformed universal characters for classical and affine algebras”, Journal of Algebra, 299:1 (2006), 33  
63. Eddy Ardonne, Rinat Kedem, Michael Stone, “Fusion products, Kostka polynomials and fermionic characters of”, J. Phys. A: Math. Gen., 38:42 (2005), 9183  
64. Taichiro Takagi, “Inverse scattering method for a soliton cellular automaton”, Nuclear Physics B, 707:3 (2005), 577  
65. J. Haglund, M. Haiman, N. Loehr, J. B. Remmel, A. Ulyanov, “A combinatorial formula for the character of the diagonal coinvariants”, Duke Math. J., 126:2 (2005)  
66. J Suzuki, “The diluteALmodels and the Φ1,2perturbation of unitary minimal CFTs”, J. Stat. Mech., 2005:01 (2005), P01004  
67. B. Feigin, M. Jimbo, R. Kedem, S. Loktev, T. Miwa, “Spaces of coinvariants and fusion product, I: From equivalence theorem to Kostka polynomials”, Duke Math. J., 125:3 (2004)  
68. B Feigin, M Jimbo, R Kedem, S Loktev, T Miwa, “Spaces of coinvariants and fusion product II. sl2 character formulas in terms of Kostka polynomials”, Journal of Algebra, 279:1 (2004), 147  
69. A.I. Molev, Handbook of Algebra, 3, 2003, 907  
70. Masato Okado, Anne Schilling, Mark Shimozono, “Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾”, Represent. Theory, 7:5 (2003), 101  
71. Eddy Ardonne, Peter Bouwknegt, Peter Dawson, “K-matrices for 2D conformal field theories”, Nuclear Physics B, 660:3 (2003), 473  
72. Anne Schilling, MathPhys Odyssey 2001, 2002, 437  
73. Goro Hatayama, Atsuo Kuniba, Masato Okado, Taichiro Takagi, “Combinatorial R Matrices for a Family of Crystals: B(1)n, D(1)n, A(2)2n, and D(2)n+1 Cases”, Journal of Algebra, 247:2 (2002), 577  
74. Goro Hatayama, Atsuo Kuniba, Masato Okado, Taichiro Takagi, Zengo Tsuboi, MathPhys Odyssey 2001, 2002, 205  
75. Anatol N. Kirillov, Anne Schilling, Mark Shimozono, The Andrews Festschrift, 2001, 209  
76. Tadeusz Lulek, Algebraic Combinatorics and Applications, 2001, 261  
77. Anne Schilling, Mark Shimozono, Formal Power Series and Algebraic Combinatorics, 2000, 367  
78. Florent Hivert, “Hecke Algebras, Difference Operators, and Quasi-Symmetric Functions”, Advances in Mathematics, 155:2 (2000), 181  
79. Goro Hatayama, Atsuo Kuniba, Masato Okado, Taichiro Takagi, Physical Combinatorics, 2000, 105  
80. Mark Shimozono, Formal Power Series and Algebraic Combinatorics, 2000, 67  
81. Peter Bouwknegt, Leung Chim, David Ridout, “Exclusion statistics in conformal field theory and the UCPF for WZW models”, Nuclear Physics B, 572:3 (2000), 547  
82. George Andrews, Anne Schilling, S. Warnaar, “An A₂ Bailey lemma and Rogers-Ramanujan-type identities”, J. Amer. Math. Soc., 12:3 (1999), 677  
83. Peter Bouwknegt, Kareljan Schoutens, “Exclusion statistics in conformal field theory — Generalized fermions and spinons for level-1 WZW theories”, Nuclear Physics B, 547:3 (1999), 501  
84. Florent Hivert, “Analogues non-commutatifs et quasi-symétriques des fonctions de Hall-Littlewood, et modules de Demazure d'une algèbre enveloppante quantique dégénérée”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:1 (1998), 1  
85. SRINANDAN DASMAHAPATRA, OMAR FODA, “STRINGS, PATHS AND STANDARD TABLEAUX”, Int. J. Mod. Phys. A, 13:03 (1998), 501  
86. Goro Hatayama, Anatol N. Kirillov, Atsuo Kuniba, Masato Okado, Taichiro Takagi, Yasuhiko Yamada, “Character formulae of sl̂n-modules and inhomogeneous paths”, Nuclear Physics B, 536:3 (1998), 575  
87. Alain Lascoux, Bernard Leclerc, Jean-Yves Thibon, “Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties”, Journal of Mathematical Physics, 38:2 (1997), 1041  
88. Atsushi Nakayashiki, Yasuhiko Yamada, “Crystallizing the spinon basis”, Commun.Math. Phys., 178:1 (1996), 179  
89. Alain Lascoux, Bernard Leclerc, Jean-Yves Thibon, “Crystal graphs andq-analogues of weight multiplicities for the root systemA n”, Lett Math Phys, 35:4 (1995), 359  
90. Susanna Fishel, “Statistics for special 𝑞,𝑡-Kostka polynomials”, Proc. Amer. Math. Soc., 123:10 (1995), 2961  
91. Frederick M Goodman, Kathleen M O'Hara, Dennis Stanton, “A unimodality identity for a Schur function”, Journal of Combinatorial Theory, Series A, 60:1 (1992), 143  
92. А. Н. Кириллов, Н. Ю. Решетихин, “Кратность весов в неприводимых тензорных представлениях полной линейной супералгебры”, Функц. анализ и его прил., 22:4 (1988), 84–85      ; A. N. Kirillov, N. Yu. Reshetikhin, “Multiplicity of weights in irreducibile tensor representations of a complete linear superalgebra”, Funct. Anal. Appl., 22:4 (1988), 328–330