Edit Profile (opens in new tab) Kirillov, Anatol N. Co-Author Distance Author ID: kirillov.anatol-n Published as: Kirillov, A. N.; Kirillov, Anatol N.; Kirillov, Anatoli more...less Homepage: http://www.kurims.kyoto-u.ac.jp/~kirillov/ External Links: MGP · Wikidata · ResearchGate · Math-Net.Ru Documents Indexed: 133 Publications since 1975, including 6 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 41 Co-Authors with 82 Joint Publications 1,079 Co-Co-Authors all top 5 Co-Authors 48 single-authored 19 Reshetikhin, Nikolai Yu. 10 Maeno, Toshiaki 6 Sakamoto, Reiho 5 Fomin, Sergey Vladimirovich 4 Kerov, Sergei V. 4 Korepin, Vladimir E. 4 Liskova, Nadejda A. 4 van Diejen, Jan Felipe 3 Kuniba, Atsuo 3 Shimozono, Mark 2 Bashmakov, M. I. 2 Berenstein, Arkady 2 Hikami, Kazuhiro 2 Isaev, Alekseĭ Petrovich 2 Nakanishi, Tomoki 2 Nenashev, Gleb V. 2 Noumi, Masatoshi 2 Schilling, Anne 2 Taneda, Makoto 2 Vostokov, Sergeĭ Vladimirovich 1 Bégin, Luc 1 Feĭgin, Boris L’vovich 1 Hatayama, Goro 1 Katsura, Hosho 1 Kawashima, Naoki 1 Lascoux, Alain 1 Leclerc, Bernard 1 Loktev, Sergey A. 1 Mathieu, Pierre 1 Naruse, Hiroshi 1 Okado, Masato 1 Scrimshaw, Travis 1 Shapiro, Boris Zalmanovich 1 Takagi, Taichiro 1 Tanaka, Shu 1 Tarasov, Vitaly Olegovich 1 Thibon, Jean-Yves 1 Tsuchiya, Akihiro 1 Umemura, Hiroshi 1 Vaintrob, Arkady 1 Walton, Mark A. all top 5 Serials 21 Journal of Soviet Mathematics 11 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 6 Letters in Mathematical Physics 5 St. Petersburg Mathematical Journal 4 Journal of Mathematical Sciences (New York) 3 Communications in Mathematical Physics 3 Discrete Mathematics 3 Nuclear Physics. B 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Journal of Physics A: Mathematical and Theoretical 2 International Journal of Modern Physics A 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 European Journal of Combinatorics 2 IMRN. International Mathematics Research Notices 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Journal of Algebraic Combinatorics 2 Zapiski Nauchnykh Seminarov POMI 2 Séminaire Lotharingien de Combinatoire 2 Moscow Mathematical Journal 1 International Journal of Modern Physics B 1 Physics Letters. B 1 Rocky Mountain Journal of Mathematics 1 Journal of Geometry and Physics 1 Advances in Mathematics 1 Duke Mathematical Journal 1 Functional Analysis and its Applications 1 Funkcialaj Ekvacioj. Serio Internacia 1 Funktsional’nyĭ Analiz i ego Prilozheniya 1 Journal of Pure and Applied Algebra 1 Mathematische Annalen 1 Mathematics of the USSR. Izvestiya 1 Proceedings of the Japan Academy. Series A 1 Tokyo Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Sūgaku 1 Leningrad Mathematical Journal 1 International Journal of Algebra and Computation 1 Automation and Remote Control 1 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Journal of Physics A: Mathematical and General 1 Selecta Mathematica. New Series 1 RIMS Kokyuroku 1 Matematicheskoe Modelirovanie 1 Problemy Analiza. Issues of Analysis all top 5 Fields 63 Combinatorics (05-XX) 32 Quantum theory (81-XX) 30 Algebraic geometry (14-XX) 23 Nonassociative rings and algebras (17-XX) 20 Special functions (33-XX) 17 Associative rings and algebras (16-XX) 16 Group theory and generalizations (20-XX) 15 Statistical mechanics, structure of matter (82-XX) 10 Topological groups, Lie groups (22-XX) 9 Partial differential equations (35-XX) 8 Number theory (11-XX) 5 Manifolds and cell complexes (57-XX) 4 Commutative algebra (13-XX) 4 Ordinary differential equations (34-XX) 4 Operator theory (47-XX) 4 Differential geometry (53-XX) 3 Convex and discrete geometry (52-XX) 2 General and overarching topics; collections (00-XX) 2 Field theory and polynomials (12-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Biology and other natural sciences (92-XX) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Difference and functional equations (39-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 107 Publications have been cited 1,625 times in 1,183 Documents Cited by ▼ Year ▼ The Yang-Baxter equation, symmetric functions, and Schubert polynomials. Zbl 0852.05078 Fomin, Sergey; Kirillov, Anatol N. 118 1996 q-Weyl group and a multiplicative formula for universal R-matrices. Zbl 0723.17014 Kirillov, A. N.; Reshetikhin, N. 103 1990 Representations of the algebra \(U_ q(sl(2))\), \(q\)-orthogonal polynomials and invariants of links. Zbl 0742.17018 Kirillov, A. N.; Reshetikhin, N. Yu. 100 1989 Quadratic algebras, Dunkl elements, and Schubert calculus. Zbl 0940.05070 Fomin, Sergey; Kirillov, Anatol N. 83 1999 Dilogarithm identities. Zbl 0894.11052 Kirillov, Anatol N. 70 1995 The Bethe Ansatz and the combinatorics of Young tableaux. Zbl 0639.20029 Kirillov, A. N.; Reshetikhin, N. Yu. 65 1988 Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras. Zbl 0900.16047 Kirillov, A. N.; Reshetikhin, N. Yu. 62 1987 Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007 Kirillov, A. N.; Berenstein, A. D. 55 1995 A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013 Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 46 2002 Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060 Fomin, Sergey; Kirillov, Anatol N. 45 1996 Introduction to tropical combinatorics. Zbl 0989.05127 Kirillov, Anatol N. 44 2001 Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025 Kirillov, A. N.; Reshetikhin, N. Yu. 35 1986 Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029 Kirillov, A. N.; Reshetikhin, N. Yu. 33 1986 The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027 Kirillov, A. N.; Reshetikhin, N. Yu. 31 1986 Affine Hecke algebras and raising operators for Macdonald polynomials. Zbl 0939.05090 Kirillov, Anatol N.; Noumi, Masatoshi 29 1998 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028 Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 28 1988 Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014 Kirillov, A. N. 27 1987 Character formulae of \(\widehat{\text{sl}}_n\)-modules and inhomogeneous paths. Zbl 0952.17013 Hatayama, Goro; Kirillov, Anatol N.; Kuniba, Atsuo; Okado, Masato; Takagi, Taichiro 26 1999 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024 Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 26 1986 Torus knot and minimal model. Zbl 1094.81550 Hikami, Kazuhiro; Kirillov, Anatol N. 24 2003 Ubiquity of Kostka polynomials. Zbl 0982.05105 Kirillov, Anatol N. 24 2001 \(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015 Kirillov, A. N.; Noumi, M. 23 1999 Notes on Schubert, Grothendieck and key polynomials. Zbl 1334.05176 Kirillov, Anatol N. 23 2016 An invitation to the generalized saturation conjecture. Zbl 1077.05098 Kirillov, Anatol N. 21 2004 Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras. Zbl 0637.16007 Kirillov, A. N.; Reshetikhin, N. Yu. 21 1987 Completeness of states of the generalized Heisenberg magnet. Zbl 0613.58014 Kirillov, A. N. 21 1987 Reduced words and plane partitions. Zbl 0882.05010 Fomin, Sergey; Kirillov, Anatol N. 19 1997 Skew Young diagram method in spectral decomposition of integrable lattice models. Zbl 0887.17008 Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 19 1997 A generalization of the Kostka-Foulkes polynomials. Zbl 0995.05146 Kirillov, Anatol N.; Shimozono, Mark 17 2002 New combinatorial formula for modified Hall-Littlewood polynomials. Zbl 0956.05101 Kirillov, Anatol N. 16 2000 On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials. Zbl 1348.05213 Kirillov, Anatol N. 16 2016 Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules. Zbl 0811.17032 Begin, L.; Kirillov, A. N.; Mathieu, P.; Walton, M. A. 15 1993 Noncommutative algebras related with Schubert calculus on Coxeter groups. Zbl 1106.05103 Kirillov, Anatol N.; Maeno, Toshiaki 13 2004 Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008 Kirillov, A. N. 13 1994 Construction of double Grothendieck polynomials of classical types using idcoxeter algebras. Zbl 1364.05081 Kirillov, Anatol N.; Naruse, Hiroshi 13 2017 On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009 Kirillov, A. N. 12 1988 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0958.05137 Kirillov, Anatol N.; Maeno, Toshiaki 11 2000 Norms of bound states. Zbl 0637.47004 Kirillov, A. N.; Korepin, V. E. 11 1988 Formulas for multiplicities of occurrence of irreducible components in the tensor product of representations of simple Lie algebras. Zbl 0860.17008 Kirillov, A. N.; Reshetikhin, N. Yu. 9 1993 On some quadratic algebras. Zbl 0966.05080 Kirillov, A. N. 9 2000 Completeness of states of the generalized Heisenberg magnet. Zbl 0538.58016 Kirillov, A. N. 9 1984 Combinatorics and geometry of higher level Weyl modules. Zbl 1129.22011 Feigin, B.; Kirillov, A. N.; Loktev, S. 9 2007 On some algebraic and combinatorial properties of Dunkl elements. Zbl 1260.13030 Kirillov, Anatol N. 9 2012 Completeness of Bethe’s states for the generalized \(XXZ\) model. Zbl 1001.82516 Kirillov, Anatol N.; Liskova, Nadejda A. 8 1997 Generating series for domino tableaux. (Séries génératrices pour les tableaux de dominos.) Zbl 0797.05079 Kirillov, Anatol N.; Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves 7 1994 Singular solutions to the Bethe ansatz equations and rigged configurations. Zbl 1302.82034 Kirillov, Anatol N.; Sakamoto, Reiho 7 2014 Unimodality of generalized Gaussian coefficients. Zbl 0768.05002 Kirillov, Anatol N. 7 1992 Skew divided difference operators and Schubert polynomials. Zbl 1146.05053 Kirillov, Anatol N. 7 2007 Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106 Kirillov, A. N.; Smirnov, F. A. 7 1989 Universal exponential solution of the Yang-Baxter equation. Zbl 0867.17009 Fomin, Sergey; Kirillov, Anatol N. 6 1996 Bethe subalgebras in Hecke algebra and Gaudin models. Zbl 1292.81077 Isaev, Alexey P.; Kirillov, Anatol N. 6 2014 Multiplicity of weights in irreducible tensor representations of a complete linear superalgebra. Zbl 0675.17013 Kirillov, A. N.; Reshetikhin, N. Yu. 6 1988 A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups. Zbl 1104.14021 Kirillov, Anatol N.; Maeno, Toshiaki 6 2005 The Clebsch-Gordan quantum coefficients. Zbl 0722.17006 Kirillov, A. N. 6 1991 Entanglement in valence-bond-solid states on symmetric graphs. Zbl 1193.82049 Katsura, Hosho; Kawashima, Naoki; Kirillov, Anatol N.; Korepin, Vladimir E.; Tanaka, Shu 6 2010 Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. Zbl 1225.16023 Kirillov, Anatol N.; Maeno, Toshiaki 6 2010 Skew Young diagram method in spectral decomposition of integrable lattice models. II: Higher levels. Zbl 1033.17018 Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 5 1998 The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032 Kirillov, A. N.; Reshetikhin, N. Yu. 5 1985 Hypergeometric generating function of \(L\)-function, Slater’s identities, and quantum invariant. Zbl 1136.11308 Hikami, K.; Kirillov, A. N. 5 2006 Generalized Umemura polynomials. Zbl 1080.33019 Kirillov, Anatol N.; Taneda, Makoto 4 2002 Quantum Schubert polynomials and quantum Schur functions. Zbl 1040.05029 Kirillov, Anatol N. 4 1999 Domino tableaux, Schützenberger involution, and the symmetric group action. Zbl 0965.05094 Berenstein, Arkady; Kirillov, Anatol N. 4 2000 Lagrange’s identity and the Hook formula. Zbl 0780.05004 Kirillov, A. N. 4 1989 Decomposition of symmetric and exterior powers of the adjoint representation of \({\mathfrak{gl}}_N\). I: Unimodality of principal specialization of the internal product of the Schur functions. Zbl 0925.17003 Kirillov, Anatol N. 4 1992 Clebsch-Gordan and Racah-Wigner coefficients for \(U_q(SU(1,1))\). Zbl 0925.17007 Liskova, N. A.; Kirillov, A. N. 4 1992 Formulas for \(q\)-spherical functions using inverse scattering theory of reflectionless Jacobi operators. Zbl 0976.33017 van Diejen, J. F.; Kirillov, A. N. 4 2000 On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063 Kirillov, Anatol N.; Maeno, Toshiaki 4 2005 Generalized Umemura polynomials and the Hirota-Miwa equation. Zbl 1029.34084 Kirillov, Anatol N.; Taneda, Makoto 3 2002 A combinatorial formula for the associated Legendre functions of integer degree. Zbl 0941.33007 van Diejen, J. F.; Kirillov, A. N. 3 2000 T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model. Zbl 0644.35084 Kirillov, A. N. 3 1988 Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin. Zbl 0644.35085 Kirillov, A. N.; Reshetikhin, N. Yu. 3 1988 Zeta-function of the mondromy for complete intersection singularities. Zbl 0597.14016 Kirillov, A. N. 3 1981 Lutz filtration of formal groups. Zbl 0337.14032 Bashmakov, M. I.; Kirillov, A. N. 3 1975 Affine nil-Hecke algebras and braided differential structure on affine Weyl groups. Zbl 1278.16036 Kirillov, Anatol N.; Maeno, Toshiaki 3 2012 Some remarks on Nepomechie-Wang eigenstates for spin 1/2 XXX model. Zbl 1336.81040 Kirillov, Anatol N.; Sakamoto, Reiho 3 2015 Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006 Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 Valance bond solid in quasicrystals. Zbl 0717.60118 Kirillov, A. N.; Korepin, V. E. 3 1990 The quantum Clebsch-Gordan coefficients. Zbl 0684.17003 Kirillov, A. N. 3 1988 Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties. Zbl 1233.05213 Kirillov, A. N.; Maeno, T. 3 2011 Bijective correspondences for rigged configurations. Zbl 0958.05135 Kirillov, A. N. 2 2000 Determinantal formulas for zonal spherical functions on hyperboloids. Zbl 0983.43007 van Diejen, J. F.; Kirillov, A. N. 2 2001 Various representations of the generalized Kostka polynomials. Zbl 0921.05067 Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 2 1999 Combinatorics of Young tableaux and configurations. Zbl 0990.05137 Kirillov, A. N. 2 2001 On some properties of Robinson-Schensted correspondence. Zbl 0778.05085 Kirillov, Anatoli 2 1991 Norm pairing in a two-dimensional local field. Zbl 0566.12006 Vostokov, S. V.; Kirillov, A. N. 2 1985 Classification of string solutions of the Bethe equations in the XXZ- model of an arbitrary spin. Zbl 0606.35070 Kirillov, A. N.; Reshetikhin, N. Yu. 2 1985 Equilibrium and control in the biocommunity species composition preservation problem. Zbl 1377.93030 Ivanova, A. S.; Kirillov, A. N. 2 2017 Bethe subalgebras in affine Birman-Murakami-Wenzl algebras and flat connections for q-KZ equations. Zbl 1357.81121 Isaev, A. P.; Kirillov, A. N.; Tarasov, V. O. 2 2016 Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019 Kirillov, Anatol N.; Sakamoto, Reiho 2 2009 Lagrange identity and Hook formula. Zbl 0689.05010 Kirillov, A. N. 2 1989 Lutz filtration of formal groups. Zbl 0342.14021 Bashmakov, M. I.; Kirillov, A. N. 1 1977 Quantum Grothendieck polynomials. Zbl 0956.14039 Kirillov, Anatol N. 1 1999 Cauchy identities for universal Schubert polynomials. Zbl 1063.05134 Kirillov, A. N. 1 2001 Bethe’s states for generalized \(XXX\) and \(XXZ\) models. Zbl 1143.82305 Kirillov, Anatol N.; Liskova, Nadejda 1 2001 Generalization of the Gale-Ryser theorem. Zbl 0980.05052 Kirillov, Anatol N. 1 2000 Physics and combinatorics. Proceedings of the Nagoya 2000 2nd international workshop, Nagoya, Japan, August 21–26, 2000. Zbl 0964.00051 1 2001 Properties of kernels of integral equations in the XXZ-model of an arbitrary spin. Zbl 0586.45002 Kirillov, A. N.; Reshetikhin, N. Yu. 1 1985 Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015 Kirillov, Anatol N.; Sakamoto, Reiho 1 2016 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0951.14507 Kirillov, Anatol N.; Maeno, Toshiaki 1 1999 Rigged configurations and Catalan, stretched parabolic Kostka numbers and polynomials: polynomiality, unimodality and log-concavity. Zbl 1409.05210 Kirillov, Anatol N. 1 2018 Rigged configurations and Catalan, stretched parabolic Kostka numbers and polynomials: polynomiality, unimodality and log-concavity. Zbl 1409.05210 Kirillov, Anatol N. 1 2018 Construction of double Grothendieck polynomials of classical types using idcoxeter algebras. Zbl 1364.05081 Kirillov, Anatol N.; Naruse, Hiroshi 13 2017 Equilibrium and control in the biocommunity species composition preservation problem. Zbl 1377.93030 Ivanova, A. S.; Kirillov, A. N. 2 2017 On \(Q\)-deformations of Postnikov-Shapiro algebras. Zbl 1385.05086 Kirillov, Anatol N.; Nenashev, Gleb 1 2017 Notes on Schubert, Grothendieck and key polynomials. Zbl 1334.05176 Kirillov, Anatol N. 23 2016 On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials. Zbl 1348.05213 Kirillov, Anatol N. 16 2016 Bethe subalgebras in affine Birman-Murakami-Wenzl algebras and flat connections for q-KZ equations. Zbl 1357.81121 Isaev, A. P.; Kirillov, A. N.; Tarasov, V. O. 2 2016 Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015 Kirillov, Anatol N.; Sakamoto, Reiho 1 2016 Some remarks on Nepomechie-Wang eigenstates for spin 1/2 XXX model. Zbl 1336.81040 Kirillov, Anatol N.; Sakamoto, Reiho 3 2015 Singular solutions to the Bethe ansatz equations and rigged configurations. Zbl 1302.82034 Kirillov, Anatol N.; Sakamoto, Reiho 7 2014 Bethe subalgebras in Hecke algebra and Gaudin models. Zbl 1292.81077 Isaev, Alexey P.; Kirillov, Anatol N. 6 2014 On some algebraic and combinatorial properties of Dunkl elements. Zbl 1260.13030 Kirillov, Anatol N. 9 2012 Affine nil-Hecke algebras and braided differential structure on affine Weyl groups. Zbl 1278.16036 Kirillov, Anatol N.; Maeno, Toshiaki 3 2012 Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties. Zbl 1233.05213 Kirillov, A. N.; Maeno, T. 3 2011 Entanglement in valence-bond-solid states on symmetric graphs. Zbl 1193.82049 Katsura, Hosho; Kawashima, Naoki; Kirillov, Anatol N.; Korepin, Vladimir E.; Tanaka, Shu 6 2010 Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. Zbl 1225.16023 Kirillov, Anatol N.; Maeno, Toshiaki 6 2010 Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019 Kirillov, Anatol N.; Sakamoto, Reiho 2 2009 Paths and Kostka-Macdonald polynomials. Zbl 1230.05287 Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 Braided differential structure on Weyl groups, quadratic algebras, and elliptic functions. Zbl 1222.47051 Kirillov, Anatol N.; Maeno, Toshiaki 1 2008 Combinatorics and geometry of higher level Weyl modules. Zbl 1129.22011 Feigin, B.; Kirillov, A. N.; Loktev, S. 9 2007 Skew divided difference operators and Schubert polynomials. Zbl 1146.05053 Kirillov, Anatol N. 7 2007 Hypergeometric generating function of \(L\)-function, Slater’s identities, and quantum invariant. Zbl 1136.11308 Hikami, K.; Kirillov, A. N. 5 2006 A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups. Zbl 1104.14021 Kirillov, Anatol N.; Maeno, Toshiaki 6 2005 On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063 Kirillov, Anatol N.; Maeno, Toshiaki 4 2005 Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006 Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 An invitation to the generalized saturation conjecture. Zbl 1077.05098 Kirillov, Anatol N. 21 2004 Noncommutative algebras related with Schubert calculus on Coxeter groups. Zbl 1106.05103 Kirillov, Anatol N.; Maeno, Toshiaki 13 2004 Torus knot and minimal model. Zbl 1094.81550 Hikami, Kazuhiro; Kirillov, Anatol N. 24 2003 A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013 Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 46 2002 A generalization of the Kostka-Foulkes polynomials. Zbl 0995.05146 Kirillov, Anatol N.; Shimozono, Mark 17 2002 Generalized Umemura polynomials. Zbl 1080.33019 Kirillov, Anatol N.; Taneda, Makoto 4 2002 Generalized Umemura polynomials and the Hirota-Miwa equation. Zbl 1029.34084 Kirillov, Anatol N.; Taneda, Makoto 3 2002 Introduction to tropical combinatorics. Zbl 0989.05127 Kirillov, Anatol N. 44 2001 Ubiquity of Kostka polynomials. Zbl 0982.05105 Kirillov, Anatol N. 24 2001 Determinantal formulas for zonal spherical functions on hyperboloids. Zbl 0983.43007 van Diejen, J. F.; Kirillov, A. N. 2 2001 Combinatorics of Young tableaux and configurations. Zbl 0990.05137 Kirillov, A. N. 2 2001 Cauchy identities for universal Schubert polynomials. Zbl 1063.05134 Kirillov, A. N. 1 2001 Bethe’s states for generalized \(XXX\) and \(XXZ\) models. Zbl 1143.82305 Kirillov, Anatol N.; Liskova, Nadejda 1 2001 Physics and combinatorics. Proceedings of the Nagoya 2000 2nd international workshop, Nagoya, Japan, August 21–26, 2000. Zbl 0964.00051 1 2001 New combinatorial formula for modified Hall-Littlewood polynomials. Zbl 0956.05101 Kirillov, Anatol N. 16 2000 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0958.05137 Kirillov, Anatol N.; Maeno, Toshiaki 11 2000 On some quadratic algebras. Zbl 0966.05080 Kirillov, A. N. 9 2000 Domino tableaux, Schützenberger involution, and the symmetric group action. Zbl 0965.05094 Berenstein, Arkady; Kirillov, Anatol N. 4 2000 Formulas for \(q\)-spherical functions using inverse scattering theory of reflectionless Jacobi operators. Zbl 0976.33017 van Diejen, J. F.; Kirillov, A. N. 4 2000 A combinatorial formula for the associated Legendre functions of integer degree. Zbl 0941.33007 van Diejen, J. F.; Kirillov, A. N. 3 2000 Bijective correspondences for rigged configurations. Zbl 0958.05135 Kirillov, A. N. 2 2000 Generalization of the Gale-Ryser theorem. Zbl 0980.05052 Kirillov, Anatol N. 1 2000 \(t\)-deformations of quantum Schubert polynomials. Zbl 1108.14307 Kirillov, Anatol N. 1 2000 Quadratic algebras, Dunkl elements, and Schubert calculus. Zbl 0940.05070 Fomin, Sergey; Kirillov, Anatol N. 83 1999 Character formulae of \(\widehat{\text{sl}}_n\)-modules and inhomogeneous paths. Zbl 0952.17013 Hatayama, Goro; Kirillov, Anatol N.; Kuniba, Atsuo; Okado, Masato; Takagi, Taichiro 26 1999 \(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015 Kirillov, A. N.; Noumi, M. 23 1999 Quantum Schubert polynomials and quantum Schur functions. Zbl 1040.05029 Kirillov, Anatol N. 4 1999 Various representations of the generalized Kostka polynomials. Zbl 0921.05067 Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 2 1999 Quantum Grothendieck polynomials. Zbl 0956.14039 Kirillov, Anatol N. 1 1999 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0951.14507 Kirillov, Anatol N.; Maeno, Toshiaki 1 1999 Affine Hecke algebras and raising operators for Macdonald polynomials. Zbl 0939.05090 Kirillov, Anatol N.; Noumi, Masatoshi 29 1998 Skew Young diagram method in spectral decomposition of integrable lattice models. II: Higher levels. Zbl 1033.17018 Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 5 1998 Reduced words and plane partitions. Zbl 0882.05010 Fomin, Sergey; Kirillov, Anatol N. 19 1997 Skew Young diagram method in spectral decomposition of integrable lattice models. Zbl 0887.17008 Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 19 1997 Completeness of Bethe’s states for the generalized \(XXZ\) model. Zbl 1001.82516 Kirillov, Anatol N.; Liskova, Nadejda A. 8 1997 The Yang-Baxter equation, symmetric functions, and Schubert polynomials. Zbl 0852.05078 Fomin, Sergey; Kirillov, Anatol N. 118 1996 Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060 Fomin, Sergey; Kirillov, Anatol N. 45 1996 Universal exponential solution of the Yang-Baxter equation. Zbl 0867.17009 Fomin, Sergey; Kirillov, Anatol N. 6 1996 Dilogarithm identities. Zbl 0894.11052 Kirillov, Anatol N. 70 1995 Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007 Kirillov, A. N.; Berenstein, A. D. 55 1995 Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008 Kirillov, A. N. 13 1994 Generating series for domino tableaux. (Séries génératrices pour les tableaux de dominos.) Zbl 0797.05079 Kirillov, Anatol N.; Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves 7 1994 Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules. Zbl 0811.17032 Begin, L.; Kirillov, A. N.; Mathieu, P.; Walton, M. A. 15 1993 Formulas for multiplicities of occurrence of irreducible components in the tensor product of representations of simple Lie algebras. Zbl 0860.17008 Kirillov, A. N.; Reshetikhin, N. Yu. 9 1993 Unimodality of generalized Gaussian coefficients. Zbl 0768.05002 Kirillov, Anatol N. 7 1992 Decomposition of symmetric and exterior powers of the adjoint representation of \({\mathfrak{gl}}_N\). I: Unimodality of principal specialization of the internal product of the Schur functions. Zbl 0925.17003 Kirillov, Anatol N. 4 1992 Clebsch-Gordan and Racah-Wigner coefficients for \(U_q(SU(1,1))\). Zbl 0925.17007 Liskova, N. A.; Kirillov, A. N. 4 1992 The Clebsch-Gordan quantum coefficients. Zbl 0722.17006 Kirillov, A. N. 6 1991 On some properties of Robinson-Schensted correspondence. Zbl 0778.05085 Kirillov, Anatoli 2 1991 q-Weyl group and a multiplicative formula for universal R-matrices. Zbl 0723.17014 Kirillov, A. N.; Reshetikhin, N. 103 1990 Valance bond solid in quasicrystals. Zbl 0717.60118 Kirillov, A. N.; Korepin, V. E. 3 1990 Representations of the algebra \(U_ q(sl(2))\), \(q\)-orthogonal polynomials and invariants of links. Zbl 0742.17018 Kirillov, A. N.; Reshetikhin, N. Yu. 100 1989 Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106 Kirillov, A. N.; Smirnov, F. A. 7 1989 Lagrange’s identity and the Hook formula. Zbl 0780.05004 Kirillov, A. N. 4 1989 Lagrange identity and Hook formula. Zbl 0689.05010 Kirillov, A. N. 2 1989 Solution of some combinatorial problems which arise in calculating correlators in exactly solvable models. Zbl 0692.35105 Kirillov, A. N.; Smirnov, F. A. 1 1989 The Bethe Ansatz and the combinatorics of Young tableaux. Zbl 0639.20029 Kirillov, A. N.; Reshetikhin, N. Yu. 65 1988 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028 Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 28 1988 On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009 Kirillov, A. N. 12 1988 Norms of bound states. Zbl 0637.47004 Kirillov, A. N.; Korepin, V. E. 11 1988 Multiplicity of weights in irreducible tensor representations of a complete linear superalgebra. Zbl 0675.17013 Kirillov, A. N.; Reshetikhin, N. Yu. 6 1988 T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model. Zbl 0644.35084 Kirillov, A. N. 3 1988 Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin. Zbl 0644.35085 Kirillov, A. N.; Reshetikhin, N. Yu. 3 1988 The quantum Clebsch-Gordan coefficients. Zbl 0684.17003 Kirillov, A. N. 3 1988 Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras. Zbl 0900.16047 Kirillov, A. N.; Reshetikhin, N. Yu. 62 1987 Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014 Kirillov, A. N. 27 1987 Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras. Zbl 0637.16007 Kirillov, A. N.; Reshetikhin, N. Yu. 21 1987 Completeness of states of the generalized Heisenberg magnet. Zbl 0613.58014 Kirillov, A. N. 21 1987 Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025 Kirillov, A. N.; Reshetikhin, N. Yu. 35 1986 Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029 Kirillov, A. N.; Reshetikhin, N. Yu. 33 1986 The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027 Kirillov, A. N.; Reshetikhin, N. Yu. 31 1986 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024 Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 26 1986 The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032 Kirillov, A. N.; Reshetikhin, N. Yu. 5 1985 Norm pairing in a two-dimensional local field. Zbl 0566.12006 Vostokov, S. V.; Kirillov, A. N. 2 1985 Classification of string solutions of the Bethe equations in the XXZ- model of an arbitrary spin. Zbl 0606.35070 Kirillov, A. N.; Reshetikhin, N. Yu. 2 1985 ...and 7 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,242 Authors 37 Kirillov, Anatol N. 20 Kuniba, Atsuo 20 Scrimshaw, Travis 19 Mészáros, Karola 18 Okado, Masato 18 Shimozono, Mark 17 Schilling, Anne 16 Hikami, Kazuhiro 15 Cao, Junpeng 15 Yang, Wenli 15 Zotov, Andrei V. 14 Kedem, Rinat 13 Li, Guangliang 13 Shi, Kangjie 12 Pak, Igor 11 Chari, Vyjayanthi 11 Di Francesco, Philippe 11 Panova, Greta 11 Sakamoto, Reiho 10 Basu-Mallick, Bireswar 10 Skovsted Buch, Anders 10 Reshetikhin, Nikolai Yu. 10 Tamvakis, Harry 10 Wang, Yupeng 10 Wheeler, Michael 9 Billey, Sara C. 9 Borodin, Alexei 9 Hao, Kun 8 Fomin, Sergey Vladimirovich 8 Greenstein, Jacob 8 Liu, Ricky Ini 8 Motegi, Kohei 8 Pechenik, Oliver 8 Pylyavskyy, Pavlo 8 Vendramin, Leandro 8 Yong, Alexander 7 Blasiak, Jonah 7 Dizier, Avery St. 7 Gould, Mark D. 7 Heckenberger, István 7 Lam, Thomas F. 7 Lapointe, Luc 7 Lenart, Cristian 7 Links, Jon Robert 7 Marberg, Eric 7 Nakanishi, Tomoki 7 Tsuboi, Zengo 7 Zinn-Justin, Paul 6 Bergeron, Nantel 6 Finkel, Federico 6 González-López, Artemio 6 Ikeda, Takeshi 6 Inoue, Rei 6 Lascoux, Alain 6 Maeno, Toshiaki 6 Matsumura, Tomoo 6 Molev, Alexander I. 6 Morse, Jennifer 6 Murakami, Hitoshi 6 Naruse, Hiroshi 6 Nepomechie, Rafael I. 6 Roby, Tom 6 Sun, Pei 6 Takagi, Taichiro 6 Warnaar, S. Ole 6 Weigandt, Anna E. 6 Xue, Panpan 6 Yamada, Yasuhiko 6 Zhang, Yaozhong 6 Zygouras, Nikolaos 5 Aggarwal, Amol 5 Alexandersson, Per 5 Anderson, Dave Edward 5 Ardonne, Eddy 5 Berenstein, Arkady 5 Brubaker, Ben 5 Bytsko, Andrei G. 5 Deguchi, Tetsuo 5 Feĭgin, Boris L’vovich 5 Frieden, Gabriel 5 Galashin, Pavel 5 Hawkes, Graham 5 Hopkins, Samuel Francis 5 Kerov, Sergei V. 5 Kozlowski, Karol Kajetan 5 Kresch, Andrew 5 Majid, Shahn 5 McNamara, Peter R. W. 5 Miller, Ezra 5 Misra, Kailash C. 5 Morales, Alejandro Henry 5 Noumi, Masatoshi 5 O’Connell, Neil 5 Pawlowski, Brendan Alexander 5 Petrov, Leonid 5 Ramadevi, Pichai 5 Rasmussen, Jorgen 5 Salisbury, Ben 5 Van Willigenburg, Stephanie J. 5 Vay, Cristian ...and 1,142 more Authors all top 5 Cited in 168 Serials 92 Nuclear Physics. B 61 Communications in Mathematical Physics 60 Advances in Mathematics 50 Journal of Algebraic Combinatorics 49 Journal of Algebra 44 Journal of Combinatorial Theory. Series A 43 Journal of Mathematical Physics 43 Letters in Mathematical Physics 41 Journal of High Energy Physics 31 The Electronic Journal of Combinatorics 27 Journal of Statistical Mechanics: Theory and Experiment 26 Duke Mathematical Journal 21 Journal of Physics A: Mathematical and Theoretical 21 Algebraic Combinatorics 20 Selecta Mathematica. New Series 19 Transactions of the American Mathematical Society 16 Journal of Geometry and Physics 15 Theoretical and Mathematical Physics 15 Journal of Soviet Mathematics 15 SIGMA. 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Proceedings Supplements 2 Documenta Mathematica 2 Vietnam Journal of Mathematics 2 Geometry & Topology 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Nonlinear Mathematical Physics ...and 68 more Serials all top 5 Cited in 52 Fields 432 Combinatorics (05-XX) 373 Nonassociative rings and algebras (17-XX) 369 Quantum theory (81-XX) 220 Statistical mechanics, structure of matter (82-XX) 217 Algebraic geometry (14-XX) 169 Associative rings and algebras (16-XX) 133 Group theory and generalizations (20-XX) 105 Special functions (33-XX) 73 Manifolds and cell complexes (57-XX) 57 Dynamical systems and ergodic theory (37-XX) 50 Number theory (11-XX) 45 Commutative algebra (13-XX) 36 Order, lattices, ordered algebraic structures (06-XX) 32 Partial differential equations (35-XX) 32 Probability theory and stochastic processes (60-XX) 31 Topological groups, Lie groups (22-XX) 28 Global analysis, analysis on manifolds (58-XX) 27 Category theory; homological algebra (18-XX) 27 Difference and functional equations (39-XX) 27 Convex and discrete geometry (52-XX) 20 \(K\)-theory (19-XX) 19 Relativity and gravitational theory (83-XX) 18 Functional analysis (46-XX) 18 Differential geometry (53-XX) 17 Ordinary differential equations (34-XX) 14 Computer science (68-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 9 Mechanics of particles and systems (70-XX) 8 Several complex variables and analytic spaces (32-XX) 7 Algebraic topology (55-XX) 6 Integral equations (45-XX) 6 Geometry (51-XX) 6 Statistics (62-XX) 5 History and biography (01-XX) 5 Functions of a complex variable (30-XX) 5 Operator theory (47-XX) 5 Numerical analysis (65-XX) 5 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 Approximations and expansions (41-XX) 2 General algebraic systems (08-XX) 2 Field theory and polynomials (12-XX) 2 Abstract harmonic analysis (43-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Fluid mechanics (76-XX) 1 Mathematical logic and foundations (03-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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