Edit Profile Kirillov, Anatol N. Compute Distance To: Compute Author ID: kirillov.anatol-n Published as: Kirillov, A. N.; Kirillov, Anatol N.; Kirillov, Anatoli Homepage: http://www.kurims.kyoto-u.ac.jp/~kirillov/ External Links: MGP · Math-Net.Ru · ResearchGate Documents Indexed: 126 Publications since 1975, including 2 Books all top 5 Co-Authors 43 single-authored 19 Reshetikhin, Nikolai Yu. 10 Maeno, Toshiaki 6 Sakamoto, Reiho 5 Fomin, Sergey Vladimirovich 4 Kerov, Sergei V. 4 Liskova, Nadejda A. 4 van Diejen, Jan Felipe 3 Korepin, Vladimir E. 3 Kuniba, Atsuo 3 Shimozono, Mark 2 Bashmakov, M. I. 2 Berenstein, Arkady 2 Hikami, Kazuhiro 2 Nakanishi, Tomoki 2 Noumi, Masatoshi 2 Schilling, Anne 2 Smirnov, Feodor A. 2 Taneda, Makoto 2 Vostokov, Sergei Vladimirovich 1 Bégin, Luc 1 Feĭgin, Boris L’vovich 1 Hatayama, Goro 1 Isaev, Alexey P. 1 Katsura, Hosho 1 Kawashima, Naoki 1 Lascoux, Alain 1 Leclerc, Bernard 1 Loktev, Sergey A. 1 Mathieu, Pierre 1 Naruse, Hiroshi 1 Nenashev, Gleb V. 1 Okado, Masato 1 Takagi, Taichiro 1 Tanaka, Shu 1 Thibon, Jean-Yves 1 Tsuchiya, Akihiro 1 Umemura, Hiroshi 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 3 Communications in Mathematical Physics 3 Discrete Mathematics 3 Nuclear Physics. B 3 Journal of Mathematical Sciences (New York) 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 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 2 Journal of Physics A: Mathematical and Theoretical 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 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Journal of Physics A: Mathematical and General 1 Selecta Mathematica. New Series 1 RIMS Kokyuroku all top 5 Fields 60 Combinatorics (05-XX) 31 Quantum theory (81-XX) 30 Algebraic geometry (14-XX) 23 Nonassociative rings and algebras (17-XX) 20 Special functions (33-XX) 16 Associative rings and algebras (16-XX) 15 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 Operator theory (47-XX) 4 Differential geometry (53-XX) 3 Commutative algebra (13-XX) 3 Ordinary differential equations (34-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) 1 Category theory; homological algebra (18-XX) 1 \(K\)-theory (19-XX) 1 Difference and functional equations (39-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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 99 Publications have been cited 1,123 times in 819 Documents Cited by ▼ Year ▼ q-Weyl group and a multiplicative formula for universal R-matrices. Zbl 0723.17014Kirillov, A. N.; Reshetikhin, N. 81 1990 The Yang-Baxter equation, symmetric functions, and Schubert polynomials. Zbl 0852.05078Fomin, Sergey; Kirillov, Anatol N. 78 1996 Representations of the algebra \(U_ q(sl(2))\), \(q\)-orthogonal polynomials and invariants of links. Zbl 0742.17018Kirillov, A. N.; Reshetikhin, N. Yu. 71 1989 Quadratic algebras, Dunkl elements, and Schubert calculus. Zbl 0940.05070Fomin, Sergey; Kirillov, Anatol N. 57 1999 Dilogarithm identities. Zbl 0894.11052Kirillov, Anatol N. 50 1995 The Bethe Ansatz and the combinatorics of Young tableaux. Zbl 0639.20029Kirillov, A. N.; Reshetikhin, N. Yu. 50 1988 A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 39 2002 Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060Fomin, Sergey; Kirillov, Anatol N. 37 1996 Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras. Zbl 0900.16047Kirillov, A. N.; Reshetikhin, N. Yu. 33 1987 Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025Kirillov, A. N.; Reshetikhin, N. Yu. 32 1986 Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007Kirillov, A. N.; Berenstein, A. D. 25 1995 Affine Hecke algebras and raising operators for Macdonald polynomials. Zbl 0939.05090Kirillov, Anatol N.; Noumi, Masatoshi 23 1998 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 22 1988 Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014Kirillov, A. N. 22 1987 The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027Kirillov, A. N.; Reshetikhin, N. Yu. 22 1986 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 22 1986 Introduction to tropical combinatorics. Zbl 0989.05127Kirillov, Anatol N. 20 2001 Character formulae of \(\widehat{\text{sl}}_n\)-modules and inhomogeneous paths. Zbl 0952.17013Hatayama, Goro; Kirillov, Anatol N.; Kuniba, Atsuo; Okado, Masato; Takagi, Taichiro 17 1999 Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029Kirillov, A. N.; Reshetikhin, N. Yu. 17 1986 Torus knot and minimal model. Zbl 1094.81550Hikami, Kazuhiro; Kirillov, Anatol N. 16 2003 A generalization of the Kostka-Foulkes polynomials. Zbl 0995.05146Kirillov, Anatol N.; Shimozono, Mark 15 2002 \(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015Kirillov, A. N.; Noumi, M. 15 1999 An invitation to the generalized saturation conjecture. Zbl 1077.05098Kirillov, Anatol N. 14 2004 Ubiquity of Kostka polynomials. Zbl 0982.05105Kirillov, Anatol N. 13 2001 Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules. Zbl 0811.17032Begin, L.; Kirillov, A. N.; Mathieu, P.; Walton, M. A. 13 1993 Notes on Schubert, Grothendieck and key polynomials. Zbl 1334.05176Kirillov, Anatol N. 12 2016 Noncommutative algebras related with Schubert calculus on Coxeter groups. Zbl 1106.05103Kirillov, Anatol N.; Maeno, Toshiaki 12 2004 New combinatorial formula for modified Hall-Littlewood polynomials. Zbl 0956.05101Kirillov, Anatol N. 12 2000 Reduced words and plane partitions. Zbl 0882.05010Fomin, Sergey; Kirillov, Anatol N. 12 1997 Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras. Zbl 0637.16007Kirillov, A. N.; Reshetikhin, N. Yu. 12 1987 Completeness of states of the generalized Heisenberg magnet. Zbl 0538.58016Kirillov, A. N. 11 1984 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0958.05137Kirillov, Anatol N.; Maeno, Toshiaki 10 2000 Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008Kirillov, A. N. 10 1994 Completeness of states of the generalized Heisenberg magnet. Zbl 0613.58014Kirillov, A. N. 10 1987 On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials. Zbl 1348.05213Kirillov, Anatol N. 9 2016 On some algebraic and combinatorial properties of Dunkl elements. Zbl 1260.13030Kirillov, Anatol N. 9 2012 Skew Young diagram method in spectral decomposition of integrable lattice models. Zbl 0887.17008Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 9 1997 Combinatorics and geometry of higher level Weyl modules. Zbl 1129.22011Feigin, B.; Kirillov, A. N.; Loktev, S. 8 2007 On some quadratic algebras. Zbl 0966.05080Kirillov, A. N. 8 2000 On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009Kirillov, A. N. 8 1988 Completeness of Bethe’s states for the generalized \(XXZ\) model. Zbl 1001.82516Kirillov, Anatol N.; Liskova, Nadejda A. 7 1997 Bethe subalgebras in Hecke algebra and Gaudin models. Zbl 1292.81077Isaev, Alexey P.; Kirillov, Anatol N. 6 2014 Generating series for domino tableaux. Zbl 0797.05079Kirillov, Anatol N.; Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves 6 1994 Formulas for multiplicities of occurrence of irreducible components in the tensor product of representations of simple Lie algebras. Zbl 0860.17008Kirillov, A. N.; Reshetikhin, N. Yu. 6 1993 Multiplicity of weights in irreducible tensor representations of a complete linear superalgebra. Zbl 0675.17013Kirillov, A. N.; Reshetikhin, N. Yu. 6 1988 Norms of bound states. Zbl 0637.47004Kirillov, A. N.; Korepin, V. E. 6 1988 Construction of double Grothendieck polynomials of classical types using idcoxeter algebras. Zbl 1364.05081Kirillov, Anatol N.; Naruse, Hiroshi 5 2017 Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. Zbl 1225.16023Kirillov, Anatol N.; Maeno, Toshiaki 5 2010 A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups. Zbl 1104.14021Kirillov, Anatol N.; Maeno, Toshiaki 5 2005 Skew Young diagram method in spectral decomposition of integrable lattice models. II: Higher levels. Zbl 1033.17018Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 5 1998 Universal exponential solution of the Yang-Baxter equation. Zbl 0867.17009Fomin, Sergey; Kirillov, Anatol N. 5 1996 Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106Kirillov, A. N.; Smirnov, F. A. 5 1989 Singular solutions to the Bethe ansatz equations and rigged configurations. Zbl 1302.82034Kirillov, Anatol N.; Sakamoto, Reiho 4 2014 Skew divided difference operators and Schubert polynomials. Zbl 1146.05053Kirillov, Anatol N. 4 2007 On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063Kirillov, Anatol N.; Maeno, Toshiaki 4 2005 Unimodality of generalized Gaussian coefficients. Zbl 0768.05002Kirillov, Anatol N. 4 1992 The Clebsch-Gordan quantum coefficients. Zbl 0722.17006Kirillov, A. N. 4 1991 Lagrange’s identity and the Hook formula. Zbl 0780.05004Kirillov, A. N. 4 1989 Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties. Zbl 1233.05213Kirillov, A. N.; Maeno, T. 3 2011 Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 Generalized Umemura polynomials. Zbl 1080.33019Kirillov, Anatol N.; Taneda, Makoto 3 2002 Formulas for \(q\)-spherical functions using inverse scattering theory of reflectionless Jacobi operators. Zbl 0976.33017van Diejen, J. F.; Kirillov, A. N. 3 2000 Quantum Schubert polynomials and quantum Schur functions. Zbl 1040.05029Kirillov, Anatol N. 3 1999 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 0925.17003Kirillov, Anatol N. 3 1992 Valance bond solid in quasicrystals. Zbl 0717.60118Kirillov, A. N.; Korepin, V. E. 3 1990 The quantum Clebsch-Gordan coefficients. Zbl 0684.17003Kirillov, A. N. 3 1988 Zeta-function of the mondromy for complete intersection singularities. Zbl 0597.14016Kirillov, A. N. 3 1981 Lutz filtration of formal groups. Zbl 0337.14032Bashmakov, M. I.; Kirillov, A. N. 3 1975 On \(Q\)-deformations of Postnikov-Shapiro algebras. Zbl 1385.05086Kirillov, Anatol N.; Nenashev, Gleb 2 2017 Bethe subalgebras in affine Birman-Murakami-Wenzl algebras and flat connections for q-KZ equations. Zbl 1357.81121Isaev, A. P.; Kirillov, A. N.; Tarasov, V. O. 2 2016 Some remarks on Nepomechie-Wang eigenstates for spin 1/2 XXX model. Zbl 1336.81040Kirillov, Anatol N.; Sakamoto, Reiho 2 2015 Affine nil-Hecke algebras and braided differential structure on affine Weyl groups. Zbl 1278.16036Kirillov, Anatol N.; Maeno, Toshiaki 2 2012 Entanglement in valence-bond-solid states on symmetric graphs. Zbl 1193.82049Katsura, Hosho; Kawashima, Naoki; Kirillov, Anatol N.; Korepin, Vladimir E.; Tanaka, Shu 2 2010 Generalized Umemura polynomials and the Hirota-Miwa equation. Zbl 1029.34084Kirillov, Anatol N.; Taneda, Makoto 2 2002 Determinantal formulas for zonal spherical functions on hyperboloids. Zbl 0983.43007van Diejen, J. F.; Kirillov, A. N. 2 2001 Domino tableaux, Schützenberger involution, and the symmetric group action. Zbl 0965.05094Berenstein, Arkady; Kirillov, Anatol N. 2 2000 A combinatorial formula for the associated Legendre functions of integer degree. Zbl 0941.33007van Diejen, J. F.; Kirillov, A. N. 2 2000 Various representations of the generalized Kostka polynomials. Zbl 0921.05067Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 2 1999 Clebsch-Gordan and Racah-Wigner coefficients for \(U_q(SU(1,1))\). Zbl 0925.17007Liskova, N. A.; Kirillov, A. N. 2 1992 Lagrange identity and Hook formula. Zbl 0689.05010Kirillov, A. N. 2 1989 T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model. Zbl 0644.35084Kirillov, A. N. 2 1988 The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032Kirillov, A. N.; Reshetikhin, N. Yu. 2 1985 Norm pairing in a two-dimensional local field. Zbl 0566.12006Vostokov, S. V.; Kirillov, A. N. 2 1985 Rigged configurations and Catalan, stretched parabolic Kostka numbers and polynomials: polynomiality, unimodality and log-concavity. Zbl 1409.05210Kirillov, Anatol N. 1 2018 Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015Kirillov, Anatol N.; Sakamoto, Reiho 1 2016 Paths and Kostka-Macdonald polynomials. Zbl 1230.05287Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 Braided differential structure on Weyl groups, quadratic algebras, and elliptic functions. Zbl 1222.47051Kirillov, Anatol N.; Maeno, Toshiaki 1 2008 Hypergeometric generating function of \(L\)-function, Slater’s identities, and quantum invariant. Zbl 1136.11308Hikami, K.; Kirillov, A. N. 1 2006 Cauchy identities for universal Schubert polynomials. Zbl 1063.05134Kirillov, A. N. 1 2001 Combinatorics of Young tableaux and configurations. Zbl 0990.05137Kirillov, A. N. 1 2001 \(t\)-deformations of quantum Schubert polynomials. Zbl 1108.14307Kirillov, Anatol N. 1 2000 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0951.14507Kirillov, Anatol N.; Maeno, Toshiaki 1 1999 On some properties of Robinson-Schensted correspondence. Zbl 0778.05085Kirillov, Anatoli 1 1991 Solution of some combinatorial problems which arise in calculating correlators in exactly solvable models. Zbl 0692.35105Kirillov, A. N.; Smirnov, F. A. 1 1989 Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin. Zbl 0644.35085Kirillov, A. N.; Reshetikhin, N. Yu. 1 1988 T-invariance, CPT-invariance and local commutativity of the quantum model \((ch\phi)_ 2\). Zbl 0606.35069Kirillov, A. N. 1 1985 Commutative formal groups. Zbl 0402.14018Kirillov, A. N. 1 1979 Lutz filtration of formal groups. Zbl 0342.14021Bashmakov, M. I.; Kirillov, A. N. 1 1977 Rigged configurations and Catalan, stretched parabolic Kostka numbers and polynomials: polynomiality, unimodality and log-concavity. Zbl 1409.05210Kirillov, Anatol N. 1 2018 Construction of double Grothendieck polynomials of classical types using idcoxeter algebras. Zbl 1364.05081Kirillov, Anatol N.; Naruse, Hiroshi 5 2017 On \(Q\)-deformations of Postnikov-Shapiro algebras. Zbl 1385.05086Kirillov, Anatol N.; Nenashev, Gleb 2 2017 Notes on Schubert, Grothendieck and key polynomials. Zbl 1334.05176Kirillov, Anatol N. 12 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 1348.05213Kirillov, Anatol N. 9 2016 Bethe subalgebras in affine Birman-Murakami-Wenzl algebras and flat connections for q-KZ equations. Zbl 1357.81121Isaev, A. P.; Kirillov, A. N.; Tarasov, V. O. 2 2016 Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015Kirillov, Anatol N.; Sakamoto, Reiho 1 2016 Some remarks on Nepomechie-Wang eigenstates for spin 1/2 XXX model. Zbl 1336.81040Kirillov, Anatol N.; Sakamoto, Reiho 2 2015 Bethe subalgebras in Hecke algebra and Gaudin models. Zbl 1292.81077Isaev, Alexey P.; Kirillov, Anatol N. 6 2014 Singular solutions to the Bethe ansatz equations and rigged configurations. Zbl 1302.82034Kirillov, Anatol N.; Sakamoto, Reiho 4 2014 On some algebraic and combinatorial properties of Dunkl elements. Zbl 1260.13030Kirillov, Anatol N. 9 2012 Affine nil-Hecke algebras and braided differential structure on affine Weyl groups. Zbl 1278.16036Kirillov, Anatol N.; Maeno, Toshiaki 2 2012 Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties. Zbl 1233.05213Kirillov, A. N.; Maeno, T. 3 2011 Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. Zbl 1225.16023Kirillov, Anatol N.; Maeno, Toshiaki 5 2010 Entanglement in valence-bond-solid states on symmetric graphs. Zbl 1193.82049Katsura, Hosho; Kawashima, Naoki; Kirillov, Anatol N.; Korepin, Vladimir E.; Tanaka, Shu 2 2010 Paths and Kostka-Macdonald polynomials. Zbl 1230.05287Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 Braided differential structure on Weyl groups, quadratic algebras, and elliptic functions. Zbl 1222.47051Kirillov, Anatol N.; Maeno, Toshiaki 1 2008 Combinatorics and geometry of higher level Weyl modules. Zbl 1129.22011Feigin, B.; Kirillov, A. N.; Loktev, S. 8 2007 Skew divided difference operators and Schubert polynomials. Zbl 1146.05053Kirillov, Anatol N. 4 2007 Hypergeometric generating function of \(L\)-function, Slater’s identities, and quantum invariant. Zbl 1136.11308Hikami, K.; Kirillov, A. N. 1 2006 A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups. Zbl 1104.14021Kirillov, Anatol N.; Maeno, Toshiaki 5 2005 On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063Kirillov, Anatol N.; Maeno, Toshiaki 4 2005 Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 An invitation to the generalized saturation conjecture. Zbl 1077.05098Kirillov, Anatol N. 14 2004 Noncommutative algebras related with Schubert calculus on Coxeter groups. Zbl 1106.05103Kirillov, Anatol N.; Maeno, Toshiaki 12 2004 Torus knot and minimal model. Zbl 1094.81550Hikami, Kazuhiro; Kirillov, Anatol N. 16 2003 A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 39 2002 A generalization of the Kostka-Foulkes polynomials. Zbl 0995.05146Kirillov, Anatol N.; Shimozono, Mark 15 2002 Generalized Umemura polynomials. Zbl 1080.33019Kirillov, Anatol N.; Taneda, Makoto 3 2002 Generalized Umemura polynomials and the Hirota-Miwa equation. Zbl 1029.34084Kirillov, Anatol N.; Taneda, Makoto 2 2002 Introduction to tropical combinatorics. Zbl 0989.05127Kirillov, Anatol N. 20 2001 Ubiquity of Kostka polynomials. Zbl 0982.05105Kirillov, Anatol N. 13 2001 Determinantal formulas for zonal spherical functions on hyperboloids. Zbl 0983.43007van Diejen, J. F.; Kirillov, A. N. 2 2001 Cauchy identities for universal Schubert polynomials. Zbl 1063.05134Kirillov, A. N. 1 2001 Combinatorics of Young tableaux and configurations. Zbl 0990.05137Kirillov, A. N. 1 2001 New combinatorial formula for modified Hall-Littlewood polynomials. Zbl 0956.05101Kirillov, Anatol N. 12 2000 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0958.05137Kirillov, Anatol N.; Maeno, Toshiaki 10 2000 On some quadratic algebras. Zbl 0966.05080Kirillov, A. N. 8 2000 Formulas for \(q\)-spherical functions using inverse scattering theory of reflectionless Jacobi operators. Zbl 0976.33017van Diejen, J. F.; Kirillov, A. N. 3 2000 Domino tableaux, Schützenberger involution, and the symmetric group action. Zbl 0965.05094Berenstein, Arkady; Kirillov, Anatol N. 2 2000 A combinatorial formula for the associated Legendre functions of integer degree. Zbl 0941.33007van Diejen, J. F.; Kirillov, A. N. 2 2000 \(t\)-deformations of quantum Schubert polynomials. Zbl 1108.14307Kirillov, Anatol N. 1 2000 Quadratic algebras, Dunkl elements, and Schubert calculus. Zbl 0940.05070Fomin, Sergey; Kirillov, Anatol N. 57 1999 Character formulae of \(\widehat{\text{sl}}_n\)-modules and inhomogeneous paths. Zbl 0952.17013Hatayama, Goro; Kirillov, Anatol N.; Kuniba, Atsuo; Okado, Masato; Takagi, Taichiro 17 1999 \(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015Kirillov, A. N.; Noumi, M. 15 1999 Quantum Schubert polynomials and quantum Schur functions. Zbl 1040.05029Kirillov, Anatol N. 3 1999 Various representations of the generalized Kostka polynomials. Zbl 0921.05067Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 2 1999 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0951.14507Kirillov, Anatol N.; Maeno, Toshiaki 1 1999 Affine Hecke algebras and raising operators for Macdonald polynomials. Zbl 0939.05090Kirillov, Anatol N.; Noumi, Masatoshi 23 1998 Skew Young diagram method in spectral decomposition of integrable lattice models. II: Higher levels. Zbl 1033.17018Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 5 1998 Reduced words and plane partitions. Zbl 0882.05010Fomin, Sergey; Kirillov, Anatol N. 12 1997 Skew Young diagram method in spectral decomposition of integrable lattice models. Zbl 0887.17008Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 9 1997 Completeness of Bethe’s states for the generalized \(XXZ\) model. Zbl 1001.82516Kirillov, Anatol N.; Liskova, Nadejda A. 7 1997 The Yang-Baxter equation, symmetric functions, and Schubert polynomials. Zbl 0852.05078Fomin, Sergey; Kirillov, Anatol N. 78 1996 Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060Fomin, Sergey; Kirillov, Anatol N. 37 1996 Universal exponential solution of the Yang-Baxter equation. Zbl 0867.17009Fomin, Sergey; Kirillov, Anatol N. 5 1996 Dilogarithm identities. Zbl 0894.11052Kirillov, Anatol N. 50 1995 Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007Kirillov, A. N.; Berenstein, A. D. 25 1995 Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008Kirillov, A. N. 10 1994 Generating series for domino tableaux. Zbl 0797.05079Kirillov, Anatol N.; Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves 6 1994 Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules. Zbl 0811.17032Begin, L.; Kirillov, A. N.; Mathieu, P.; Walton, M. A. 13 1993 Formulas for multiplicities of occurrence of irreducible components in the tensor product of representations of simple Lie algebras. Zbl 0860.17008Kirillov, A. N.; Reshetikhin, N. Yu. 6 1993 Unimodality of generalized Gaussian coefficients. Zbl 0768.05002Kirillov, Anatol N. 4 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 0925.17003Kirillov, Anatol N. 3 1992 Clebsch-Gordan and Racah-Wigner coefficients for \(U_q(SU(1,1))\). Zbl 0925.17007Liskova, N. A.; Kirillov, A. N. 2 1992 The Clebsch-Gordan quantum coefficients. Zbl 0722.17006Kirillov, A. N. 4 1991 On some properties of Robinson-Schensted correspondence. Zbl 0778.05085Kirillov, Anatoli 1 1991 q-Weyl group and a multiplicative formula for universal R-matrices. Zbl 0723.17014Kirillov, A. N.; Reshetikhin, N. 81 1990 Valance bond solid in quasicrystals. Zbl 0717.60118Kirillov, A. N.; Korepin, V. E. 3 1990 Representations of the algebra \(U_ q(sl(2))\), \(q\)-orthogonal polynomials and invariants of links. Zbl 0742.17018Kirillov, A. N.; Reshetikhin, N. Yu. 71 1989 Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106Kirillov, A. N.; Smirnov, F. A. 5 1989 Lagrange’s identity and the Hook formula. Zbl 0780.05004Kirillov, A. N. 4 1989 Lagrange identity and Hook formula. Zbl 0689.05010Kirillov, A. N. 2 1989 Solution of some combinatorial problems which arise in calculating correlators in exactly solvable models. Zbl 0692.35105Kirillov, A. N.; Smirnov, F. A. 1 1989 The Bethe Ansatz and the combinatorics of Young tableaux. Zbl 0639.20029Kirillov, A. N.; Reshetikhin, N. Yu. 50 1988 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 22 1988 On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009Kirillov, A. N. 8 1988 Multiplicity of weights in irreducible tensor representations of a complete linear superalgebra. Zbl 0675.17013Kirillov, A. N.; Reshetikhin, N. Yu. 6 1988 Norms of bound states. Zbl 0637.47004Kirillov, A. N.; Korepin, V. E. 6 1988 The quantum Clebsch-Gordan coefficients. Zbl 0684.17003Kirillov, A. N. 3 1988 T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model. Zbl 0644.35084Kirillov, A. N. 2 1988 Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin. Zbl 0644.35085Kirillov, A. N.; Reshetikhin, N. Yu. 1 1988 Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras. Zbl 0900.16047Kirillov, A. N.; Reshetikhin, N. Yu. 33 1987 Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014Kirillov, A. N. 22 1987 Representation of Yangians and multiplicities of occurrence of irreducible components of the tensor product of simple algebras. Zbl 0637.16007Kirillov, A. N.; Reshetikhin, N. Yu. 12 1987 Completeness of states of the generalized Heisenberg magnet. Zbl 0613.58014Kirillov, A. N. 10 1987 Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025Kirillov, A. N.; Reshetikhin, N. Yu. 32 1986 The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027Kirillov, A. N.; Reshetikhin, N. Yu. 22 1986 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 22 1986 Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029Kirillov, A. N.; Reshetikhin, N. Yu. 17 1986 The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032Kirillov, A. N.; Reshetikhin, N. Yu. 2 1985 Norm pairing in a two-dimensional local field. Zbl 0566.12006Vostokov, S. V.; Kirillov, A. N. 2 1985 T-invariance, CPT-invariance and local commutativity of the quantum model \((ch\phi)_ 2\). Zbl 0606.35069Kirillov, A. N. 1 1985 Completeness of states of the generalized Heisenberg magnet. Zbl 0538.58016Kirillov, A. N. 11 1984 Zeta-function of the mondromy for complete intersection singularities. Zbl 0597.14016Kirillov, A. N. 3 1981 Commutative formal groups. Zbl 0402.14018Kirillov, A. N. 1 1979 Lutz filtration of formal groups. Zbl 0342.14021Bashmakov, M. I.; Kirillov, A. N. 1 1977 Lutz filtration of formal groups. Zbl 0337.14032Bashmakov, M. I.; Kirillov, A. N. 3 1975 all cited Publications top 5 cited Publications all top 5 Cited by 897 Authors 36 Kirillov, Anatol N. 18 Kuniba, Atsuo 15 Okado, Masato 15 Schilling, Anne 14 Hikami, Kazuhiro 14 Scrimshaw, Travis 14 Shimozono, Mark 11 Sakamoto, Reiho 10 Kedem, Rinat 10 Mészáros, Karola 10 Pak, Igor 9 Skovsted Buch, Anders 8 Chari, Vyjayanthi 8 Di Francesco, Philippe 8 Fomin, Sergey Vladimirovich 8 Reshetikhin, Nikolai Yu. 8 Tamvakis, Harry 7 Billey, Sara C. 7 Greenstein, Jacob 7 Lapointe, Luc 7 Nakanishi, Tomoki 7 Panova, Greta 7 Yong, Alexander 7 Zinn-Justin, Paul 6 Gould, Mark D. 6 Inoue, Rei 6 Lam, Thomas F. 6 Lascoux, Alain 6 Lenart, Cristian 6 Maeno, Toshiaki 6 Matsumura, Tomoo 6 Molev, Alexander I. 6 Naruse, Hiroshi 6 Pylyavskyy, Pavlo 6 Takagi, Taichiro 6 Vendramin, Leandro 6 Wheeler, Michael 5 Anderson, Dave Edward 5 Berenstein, Arkady 5 Bergeron, Nantel 5 Blasiak, Jonah 5 Bytsko, Andrei G. 5 Heckenberger, István 5 Ikeda, Takeshi 5 Kerov, Sergei V. 5 Kresch, Andrew 5 Majid, Shahn 5 Miller, Ezra 5 Pechenik, Oliver 5 Van Willigenburg, Stephanie J. 5 Vay, Cristian 5 Warnaar, S. Ole 5 Yang, Wenli 5 Zhang, Ruibin 5 Zhang, Yaozhong 4 Alexandersson, Per 4 Andruskiewitsch, Nicolás 4 Bazhanov, Vladimir V. 4 Cao, Junpeng 4 Feĭgin, Boris L’vovich 4 Frenkel, Igor B. 4 Galashin, Pavel 4 Hao, Kun 4 Khoroshkin, Sergey M. 4 Levendorskiĭ, Sergeĭ Zakharovich 4 Li, Guangliang 4 Links, Jon Robert 4 Liu, Ricky Ini 4 Loktev, Sergey A. 4 Lyakhovskiĭ, Vladimir Dmitrievich 4 Mathieu, Pierre 4 McNamara, Peter R. W. 4 Milas, Antun 4 Morales, Alejandro H. 4 Morse, Jennifer 4 Murakami, Hitoshi 4 Nazarov, Maxim Leonidovich 4 Nepomechie, Rafael I. 4 Noumi, Masatoshi 4 O’Connell, Neil 4 Salisbury, Ben 4 Shi, Kangjie 4 Sottile, Frank 4 Yamane, Hiroyuki 4 Zotov, Andrei V. 3 Angiono, Iván Ezequiel 3 Ardonne, Eddy 3 Basu-Mallick, Bireswar 3 Borodin, Alexei 3 Brubaker, Ben 3 Bump, Daniel 3 Ciocan-Fontanine, Ionuţ 3 Clarkson, Peter A. 3 Corwin, Ivan 3 Deguchi, Tetsuo 3 Foda, Omar 3 Frahm, Holger 3 Fulton, William 3 García Iglesias, Agustín 3 Graña, Matías ...and 797 more Authors all top 5 Cited in 132 Serials 54 Communications in Mathematical Physics 51 Advances in Mathematics 50 Nuclear Physics. B 45 Journal of Algebraic Combinatorics 43 Journal of Mathematical Physics 41 Journal of Algebra 41 Journal of Combinatorial Theory. Series A 39 Letters in Mathematical Physics 27 Journal of High Energy Physics 25 Duke Mathematical Journal 16 Transactions of the American Mathematical Society 15 Journal of Geometry and Physics 15 Journal of Soviet Mathematics 13 Discrete Mathematics 12 Algebraic Combinatorics 11 Proceedings of the American Mathematical Society 11 Journal of Statistical Mechanics: Theory and Experiment 10 Séminaire Lotharingien de Combinatoire 10 Algebras and Representation Theory 9 Theoretical and Mathematical Physics 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 9 European Journal of Combinatorics 9 Journal of the American Mathematical Society 9 Journal of Mathematical Sciences (New York) 9 The Electronic Journal of Combinatorics 8 Journal of Pure and Applied Algebra 8 Mathematische Zeitschrift 8 Selecta Mathematica. New Series 7 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 6 Advances in Applied Mathematics 6 Journal of Physics A: Mathematical and Theoretical 5 International Journal of Modern Physics A 5 Physics Letters. B 5 Inventiones Mathematicae 5 SIAM Journal on Discrete Mathematics 5 St. Petersburg Mathematical Journal 5 Annals of Combinatorics 5 Annales Henri Poincaré 5 Algebraic & Geometric Topology 4 Communications in Algebra 4 International Journal of Mathematics 4 Representation Theory 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Journal of Statistical Physics 3 Reviews in Mathematical Physics 3 Annales de l’Institut Fourier 3 Journal of Computational and Applied Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Annalen 3 Topology and its Applications 3 Transformation Groups 3 The Ramanujan Journal 3 Research in the Mathematical Sciences 2 International Journal of Modern Physics B 2 International Journal of Theoretical Physics 2 Rocky Mountain Journal of Mathematics 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of the Mathematical Society of Japan 2 Nagoya Mathematical Journal 2 Proceedings of the Japan Academy. Series A 2 Rendiconti del Seminario Matematico della Università di Padova 2 Acta Applicandae Mathematicae 2 Journal of Symbolic Computation 2 Probability Theory and Related Fields 2 Linear Algebra and its Applications 2 Proceedings of the National Academy of Sciences of the United States of America 2 Experimental Mathematics 2 Geometry & Topology 2 New Journal of Physics 2 Quantum Topology 1 Modern Physics Letters A 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Physica A 1 Physics Letters. A 1 Reports on Mathematical Physics 1 Russian Mathematical Surveys 1 Chaos, Solitons and Fractals 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Probability 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Canadian Journal of Mathematics 1 Compositio Mathematica 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 Kodai Mathematical Journal 1 Manuscripta Mathematica 1 Memoirs of the American Mathematical Society 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Chinese Annals of Mathematics. Series B 1 Discrete & Computational Geometry 1 Mathematical and Computer Modelling ...and 32 more Serials all top 5 Cited in 46 Fields 309 Combinatorics (05-XX) 280 Nonassociative rings and algebras (17-XX) 246 Quantum theory (81-XX) 146 Algebraic geometry (14-XX) 127 Statistical mechanics, structure of matter (82-XX) 124 Associative rings and algebras (16-XX) 92 Group theory and generalizations (20-XX) 76 Special functions (33-XX) 53 Manifolds and cell complexes (57-XX) 37 Dynamical systems and ergodic theory (37-XX) 34 Number theory (11-XX) 33 Commutative algebra (13-XX) 25 Global analysis, analysis on manifolds (58-XX) 19 Topological groups, Lie groups (22-XX) 19 Partial differential equations (35-XX) 18 Order, lattices, ordered algebraic structures (06-XX) 18 Category theory; homological algebra (18-XX) 18 Convex and discrete geometry (52-XX) 14 Difference and functional equations (39-XX) 14 Functional analysis (46-XX) 13 \(K\)-theory (19-XX) 13 Differential geometry (53-XX) 13 Probability theory and stochastic processes (60-XX) 11 Ordinary differential equations (34-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Relativity and gravitational theory (83-XX) 9 Computer science (68-XX) 7 Several complex variables and analytic spaces (32-XX) 6 Algebraic topology (55-XX) 5 Geometry (51-XX) 5 Information and communication theory, circuits (94-XX) 4 Operator theory (47-XX) 4 Statistics (62-XX) 4 Mechanics of particles and systems (70-XX) 3 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 2 General and overarching topics; collections (00-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Numerical analysis (65-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year