Edit Profile (opens in new tab) Kirillov, Anatol N. Compute Distance To: Compute 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 · ResearchGate · Math-Net.Ru Documents Indexed: 125 Publications since 1975 2 Contributions as Editor Co-Authors: 38 Co-Authors with 79 Joint Publications 836 Co-Co-Authors all top 5 Co-Authors 44 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 Isaev, Alekseĭ Petrovich 2 Nakanishi, Tomoki 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 Nenashev, Gleb V. 1 Okado, Masato 1 Takagi, Taichiro 1 Tanaka, Shu 1 Tarasov, Vitaly Olegovich 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 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 60 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 Ordinary differential equations (34-XX) 4 Operator theory (47-XX) 4 Differential geometry (53-XX) 3 Commutative algebra (13-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 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 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 100 Publications have been cited 1,213 times in 884 Documents Cited by ▼ Year ▼ The Yang-Baxter equation, symmetric functions, and Schubert polynomials. Zbl 0852.05078Fomin, Sergey; Kirillov, Anatol N. 91 1996 q-Weyl group and a multiplicative formula for universal R-matrices. Zbl 0723.17014Kirillov, A. N.; Reshetikhin, N. 86 1990 Representations of the algebra \(U_ q(sl(2))\), \(q\)-orthogonal polynomials and invariants of links. Zbl 0742.17018Kirillov, A. N.; Reshetikhin, N. Yu. 73 1989 Quadratic algebras, Dunkl elements, and Schubert calculus. Zbl 0940.05070Fomin, Sergey; Kirillov, Anatol N. 64 1999 Dilogarithm identities. Zbl 0894.11052Kirillov, Anatol N. 55 1995 The Bethe Ansatz and the combinatorics of Young tableaux. Zbl 0639.20029Kirillov, A. N.; Reshetikhin, N. Yu. 53 1988 A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 41 2002 Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060Fomin, Sergey; Kirillov, Anatol N. 41 1996 Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025Kirillov, A. N.; Reshetikhin, N. Yu. 33 1986 Introduction to tropical combinatorics. Zbl 0989.05127Kirillov, Anatol N. 30 2001 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. 29 1987 Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007Kirillov, A. N.; Berenstein, A. D. 27 1995 The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027Kirillov, A. N.; Reshetikhin, N. Yu. 25 1986 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 24 1986 Affine Hecke algebras and raising operators for Macdonald polynomials. Zbl 0939.05090Kirillov, Anatol N.; Noumi, Masatoshi 24 1998 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 23 1988 Character formulae of \(\widehat{\text{sl}}_n\)-modules and inhomogeneous paths. Zbl 0952.17013Hatayama, Goro; Kirillov, Anatol N.; Kuniba, Atsuo; Okado, Masato; Takagi, Taichiro 21 1999 Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014Kirillov, A. N. 20 1987 Torus knot and minimal model. Zbl 1094.81550Hikami, Kazuhiro; Kirillov, Anatol N. 19 2003 An invitation to the generalized saturation conjecture. Zbl 1077.05098Kirillov, Anatol N. 17 2004 Ubiquity of Kostka polynomials. Zbl 0982.05105Kirillov, Anatol N. 17 2001 \(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015Kirillov, A. N.; Noumi, M. 17 1999 Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029Kirillov, A. N.; Reshetikhin, N. Yu. 17 1986 Notes on Schubert, Grothendieck and key polynomials. Zbl 1334.05176Kirillov, Anatol N. 16 2016 Reduced words and plane partitions. Zbl 0882.05010Fomin, Sergey; Kirillov, Anatol N. 16 1997 A generalization of the Kostka-Foulkes polynomials. Zbl 0995.05146Kirillov, Anatol N.; Shimozono, Mark 15 2002 New combinatorial formula for modified Hall-Littlewood polynomials. Zbl 0956.05101Kirillov, Anatol N. 14 2000 Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules. Zbl 0811.17032Begin, L.; Kirillov, A. N.; Mathieu, P.; Walton, M. A. 13 1993 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 Noncommutative algebras related with Schubert calculus on Coxeter groups. Zbl 1106.05103Kirillov, Anatol N.; Maeno, Toshiaki 12 2004 Completeness of states of the generalized Heisenberg magnet. Zbl 0613.58014Kirillov, A. N. 11 1987 Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008Kirillov, A. N. 10 1994 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. 10 2016 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0958.05137Kirillov, Anatol N.; Maeno, Toshiaki 10 2000 Skew Young diagram method in spectral decomposition of integrable lattice models. Zbl 0887.17008Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki 9 1997 On some algebraic and combinatorial properties of Dunkl elements. Zbl 1260.13030Kirillov, Anatol N. 9 2012 On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009Kirillov, A. N. 9 1988 Completeness of states of the generalized Heisenberg magnet. Zbl 0538.58016Kirillov, A. N. 9 1984 Norms of bound states. Zbl 0637.47004Kirillov, A. N.; Korepin, V. E. 8 1988 Combinatorics and geometry of higher level Weyl modules. Zbl 1129.22011Feigin, B.; Kirillov, A. N.; Loktev, S. 8 2007 Construction of double Grothendieck polynomials of classical types using idcoxeter algebras. Zbl 1364.05081Kirillov, Anatol N.; Naruse, Hiroshi 8 2017 Generating series for domino tableaux. (Séries génératrices pour les tableaux de dominos.) Zbl 0797.05079Kirillov, Anatol N.; Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves 7 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. 7 1993 On some quadratic algebras. Zbl 0966.05080Kirillov, A. N. 7 2000 Completeness of Bethe’s states for the generalized \(XXZ\) model. Zbl 1001.82516Kirillov, Anatol N.; Liskova, Nadejda A. 6 1997 Bethe subalgebras in Hecke algebra and Gaudin models. Zbl 1292.81077Isaev, Alexey P.; Kirillov, Anatol N. 6 2014 Multiplicity of weights in irreducible tensor representations of a complete linear superalgebra. Zbl 0675.17013Kirillov, A. N.; Reshetikhin, N. Yu. 6 1988 A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups. Zbl 1104.14021Kirillov, Anatol N.; Maeno, Toshiaki 5 2005 Unimodality of generalized Gaussian coefficients. Zbl 0768.05002Kirillov, Anatol N. 5 1992 Universal exponential solution of the Yang-Baxter equation. Zbl 0867.17009Fomin, Sergey; Kirillov, Anatol N. 5 1996 Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. Zbl 1225.16023Kirillov, Anatol N.; Maeno, Toshiaki 5 2010 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 Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106Kirillov, A. N.; Smirnov, F. A. 5 1989 Generalized Umemura polynomials. Zbl 1080.33019Kirillov, Anatol N.; Taneda, Makoto 4 2002 The Clebsch-Gordan quantum coefficients. Zbl 0722.17006Kirillov, A. N. 4 1991 Formulas for \(q\)-spherical functions using inverse scattering theory of reflectionless Jacobi operators. Zbl 0976.33017van Diejen, J. F.; Kirillov, A. N. 4 2000 Skew divided difference operators and Schubert polynomials. Zbl 1146.05053Kirillov, Anatol N. 4 2007 Quantum Schubert polynomials and quantum Schur functions. Zbl 1040.05029Kirillov, Anatol N. 4 1999 Singular solutions to the Bethe ansatz equations and rigged configurations. Zbl 1302.82034Kirillov, Anatol N.; Sakamoto, Reiho 4 2014 Generalized Umemura polynomials and the Hirota-Miwa equation. Zbl 1029.34084Kirillov, Anatol N.; Taneda, Makoto 3 2002 Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 Zeta-function of the mondromy for complete intersection singularities. Zbl 0597.14016Kirillov, A. N. 3 1981 A combinatorial formula for the associated Legendre functions of integer degree. Zbl 0941.33007van Diejen, J. F.; Kirillov, A. N. 3 2000 Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties. Zbl 1233.05213Kirillov, A. N.; Maeno, T. 3 2011 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 Lutz filtration of formal groups. Zbl 0337.14032Bashmakov, M. I.; Kirillov, A. N. 3 1975 On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 The quantum Clebsch-Gordan coefficients. Zbl 0684.17003Kirillov, A. N. 3 1988 Valance bond solid in quasicrystals. Zbl 0717.60118Kirillov, A. N.; Korepin, V. E. 3 1990 Equilibrium and control in the biocommunity species composition preservation problem. Zbl 1377.93030Ivanova, A. S.; Kirillov, A. N. 2 2017 Hypergeometric generating function of \(L\)-function, Slater’s identities, and quantum invariant. Zbl 1136.11308Hikami, K.; Kirillov, A. N. 2 2006 T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model. Zbl 0644.35084Kirillov, A. N. 2 1988 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 Domino tableaux, Schützenberger involution, and the symmetric group action. Zbl 0965.05094Berenstein, Arkady; Kirillov, Anatol N. 2 2000 Determinantal formulas for zonal spherical functions on hyperboloids. Zbl 0983.43007van Diejen, J. F.; Kirillov, A. N. 2 2001 Clebsch-Gordan and Racah-Wigner coefficients for \(U_q(SU(1,1))\). Zbl 0925.17007Liskova, N. A.; Kirillov, A. N. 2 1992 Some remarks on Nepomechie-Wang eigenstates for spin 1/2 XXX model. Zbl 1336.81040Kirillov, Anatol N.; Sakamoto, Reiho 2 2015 Various representations of the generalized Kostka polynomials. Zbl 0921.05067Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 2 1999 Norm pairing in a two-dimensional local field. Zbl 0566.12006Vostokov, S. V.; Kirillov, A. N. 2 1985 The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032Kirillov, A. N.; Reshetikhin, N. Yu. 2 1985 Lagrange identity and Hook formula. Zbl 0689.05010Kirillov, A. N. 2 1989 Affine nil-Hecke algebras and braided differential structure on affine Weyl groups. Zbl 1278.16036Kirillov, Anatol N.; Maeno, Toshiaki 2 2012 Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015Kirillov, Anatol N.; Sakamoto, Reiho 1 2016 Lagrange’s identity and the Hook formula. Zbl 0780.05004Kirillov, A. N. 1 1989 Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 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 On some properties of Robinson-Schensted correspondence. Zbl 0778.05085Kirillov, Anatoli 1 1991 Paths and Kostka-Macdonald polynomials. Zbl 1230.05287Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 Cauchy identities for universal Schubert polynomials. Zbl 1063.05134Kirillov, A. N. 1 2001 \(t\)-deformations of quantum Schubert polynomials. Zbl 1108.14307Kirillov, Anatol N. 1 2000 T-invariance, CPT-invariance and local commutativity of the quantum model \((ch\phi)_ 2\). Zbl 0606.35069Kirillov, A. N. 1 1985 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. 1 2016 Combinatorics of Young tableaux and configurations. Zbl 0990.05137Kirillov, A. N. 1 2001 Rigged configurations and Catalan, stretched parabolic Kostka numbers and polynomials: polynomiality, unimodality and log-concavity. Zbl 1409.05210Kirillov, Anatol N. 1 2018 Commutative formal groups. Zbl 0402.14018Kirillov, A. N. 1 1979 Braided differential structure on Weyl groups, quadratic algebras, and elliptic functions. Zbl 1222.47051Kirillov, Anatol N.; Maeno, Toshiaki 1 2008 Lutz filtration of formal groups. Zbl 0342.14021Bashmakov, M. I.; Kirillov, A. N. 1 1977 Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0951.14507Kirillov, Anatol N.; Maeno, Toshiaki 1 1999 On \(Q\)-deformations of Postnikov-Shapiro algebras. Zbl 1385.05086Kirillov, Anatol N.; Nenashev, Gleb 1 2017 Solution of some combinatorial problems which arise in calculating correlators in exactly solvable models. Zbl 0692.35105Kirillov, A. N.; Smirnov, F. A. 1 1989 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 8 2017 Equilibrium and control in the biocommunity species composition preservation problem. Zbl 1377.93030Ivanova, A. S.; Kirillov, A. N. 2 2017 On \(Q\)-deformations of Postnikov-Shapiro algebras. Zbl 1385.05086Kirillov, Anatol N.; Nenashev, Gleb 1 2017 Notes on Schubert, Grothendieck and key polynomials. Zbl 1334.05176Kirillov, Anatol N. 16 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. 10 2016 Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015Kirillov, Anatol N.; Sakamoto, Reiho 1 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. 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 Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019Kirillov, Anatol N.; Sakamoto, Reiho 1 2009 Paths and Kostka-Macdonald polynomials. Zbl 1230.05287Kirillov, 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. 2 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 Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063Kirillov, Anatol N.; Maeno, Toshiaki 3 2005 An invitation to the generalized saturation conjecture. Zbl 1077.05098Kirillov, Anatol N. 17 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. 19 2003 A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark 41 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 4 2002 Generalized Umemura polynomials and the Hirota-Miwa equation. Zbl 1029.34084Kirillov, Anatol N.; Taneda, Makoto 3 2002 Introduction to tropical combinatorics. Zbl 0989.05127Kirillov, Anatol N. 30 2001 Ubiquity of Kostka polynomials. Zbl 0982.05105Kirillov, Anatol N. 17 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. 14 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. 7 2000 Formulas for \(q\)-spherical functions using inverse scattering theory of reflectionless Jacobi operators. Zbl 0976.33017van Diejen, J. F.; Kirillov, A. N. 4 2000 A combinatorial formula for the associated Legendre functions of integer degree. Zbl 0941.33007van 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 \(t\)-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. 64 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 21 1999 \(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015Kirillov, A. N.; Noumi, M. 17 1999 Quantum Schubert polynomials and quantum Schur functions. Zbl 1040.05029Kirillov, Anatol N. 4 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 24 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. 16 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. 6 1997 The Yang-Baxter equation, symmetric functions, and Schubert polynomials. Zbl 0852.05078Fomin, Sergey; Kirillov, Anatol N. 91 1996 Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060Fomin, Sergey; Kirillov, Anatol N. 41 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. 55 1995 Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007Kirillov, A. N.; Berenstein, A. D. 27 1995 Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008Kirillov, A. N. 10 1994 Generating series for domino tableaux. (Séries génératrices pour les tableaux de dominos.) Zbl 0797.05079Kirillov, Anatol N.; Lascoux, Alain; Leclerc, Bernard; Thibon, Jean-Yves 7 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. 7 1993 Unimodality of generalized Gaussian coefficients. Zbl 0768.05002Kirillov, Anatol N. 5 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. 86 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. 73 1989 Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106Kirillov, A. N.; Smirnov, F. A. 5 1989 Lagrange identity and Hook formula. Zbl 0689.05010Kirillov, A. N. 2 1989 Lagrange’s identity and the Hook formula. Zbl 0780.05004Kirillov, A. N. 1 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. 53 1988 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 23 1988 On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009Kirillov, A. N. 9 1988 Norms of bound states. Zbl 0637.47004Kirillov, A. N.; Korepin, V. E. 8 1988 Multiplicity of weights in irreducible tensor representations of a complete linear superalgebra. Zbl 0675.17013Kirillov, A. N.; Reshetikhin, N. Yu. 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. 29 1987 Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014Kirillov, A. N. 20 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. 11 1987 Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025Kirillov, A. N.; Reshetikhin, N. Yu. 33 1986 The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027Kirillov, A. N.; Reshetikhin, N. Yu. 25 1986 Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu. 24 1986 Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029Kirillov, A. N.; Reshetikhin, N. Yu. 17 1986 Norm pairing in a two-dimensional local field. Zbl 0566.12006Vostokov, S. V.; Kirillov, A. N. 2 1985 The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032Kirillov, A. N.; Reshetikhin, N. Yu. 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. 9 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 955 Authors 36 Kirillov, Anatol N. 18 Kuniba, Atsuo 18 Scrimshaw, Travis 17 Schilling, Anne 16 Mészáros, Karola 15 Okado, Masato 15 Shimozono, Mark 13 Hikami, Kazuhiro 11 Sakamoto, Reiho 9 Skovsted Buch, Anders 9 Kedem, Rinat 9 Pak, Igor 9 Panova, Greta 8 Billey, Sara C. 8 Chari, Vyjayanthi 8 Fomin, Sergey Vladimirovich 8 Reshetikhin, Nikolai Yu. 8 Tamvakis, Harry 7 Di Francesco, Philippe 7 Lam, Thomas F. 7 Lapointe, Luc 7 Nakanishi, Tomoki 7 Yong, Alexander 7 Zinn-Justin, Paul 6 Gould, Mark D. 6 Greenstein, Jacob 6 Inoue, Rei 6 Lascoux, Alain 6 Maeno, Toshiaki 6 Matsumura, Tomoo 6 Naruse, Hiroshi 6 Pechenik, Oliver 6 Pylyavskyy, Pavlo 6 Takagi, Taichiro 6 Vendramin, Leandro 6 Warnaar, S. Ole 6 Wheeler, Michael 5 Anderson, Dave Edward 5 Berenstein, Arkady 5 Bergeron, Nantel 5 Blasiak, Jonah 5 Bytsko, Andrei G. 5 Dizier, Avery St. 5 Galashin, Pavel 5 Heckenberger, István 5 Ikeda, Takeshi 5 Kerov, Sergei V. 5 Kresch, Andrew 5 Lenart, Cristian 5 Liu, Ricky Ini 5 Majid, Shahn 5 McNamara, Peter R. W. 5 Miller, Ezra 5 Molev, Alexander I. 5 Morales, Alejandro Henry 5 Murakami, Hitoshi 5 Noumi, Masatoshi 5 O’Connell, Neil 5 Salisbury, Ben 5 Van Willigenburg, Stephanie J. 5 Vay, Cristian 5 Yang, Wenli 5 Zhang, Ruibin 5 Zhang, Yaozhong 5 Zotov, Andrei V. 4 Alexandersson, Per 4 Andruskiewitsch, Nicolás 4 Cao, Junpeng 4 Feĭgin, Boris L’vovich 4 Frenkel, Igor B. 4 Frieden, Gabriel 4 Hao, Kun 4 Hawkes, Graham 4 Levendorskiĭ, Sergeĭ Zakharovich 4 Li, Guangliang 4 Links, Jon Robert 4 Loktev, Sergey A. 4 Lyakhovskiĭ, Vladimir Dmitrievich 4 Marberg, Eric 4 Mathieu, Pierre 4 Milas, Antun 4 Morse, Jennifer 4 Nazarov, Maxim Leonidovich 4 Nepomechie, Rafael I. 4 Petrov, Leonid 4 Postnikov, Alexander 4 Roby, Tom 4 Shi, Kangjie 4 Sottile, Frank 4 Vinet, Luc 4 Weigandt, Anna E. 4 Yamada, Yasuhiko 4 Yamane, Hiroyuki 4 Zygouras, Nikolaos 3 Angiono, Iván Ezequiel 3 Ardonne, Eddy 3 Basu-Mallick, Bireswar 3 Borodin, Alexei 3 Brubaker, Ben 3 Bump, Daniel ...and 855 more Authors all top 5 Cited in 139 Serials 57 Communications in Mathematical Physics 51 Nuclear Physics. B 51 Advances in Mathematics 47 Journal of Algebraic Combinatorics 43 Journal of Mathematical Physics 40 Letters in Mathematical Physics 40 Journal of Algebra 39 Journal of Combinatorial Theory. Series A 26 The Electronic Journal of Combinatorics 25 Duke Mathematical Journal 25 Journal of High Energy Physics 18 Transactions of the American Mathematical Society 16 Journal of Geometry and Physics 15 Journal of Soviet Mathematics 15 Algebraic Combinatorics 12 Discrete Mathematics 12 Journal of Statistical Mechanics: Theory and Experiment 11 Mathematische Zeitschrift 11 Selecta Mathematica. New Series 10 Theoretical and Mathematical Physics 10 Proceedings of the American Mathematical Society 10 European Journal of Combinatorics 10 Journal of Mathematical Sciences (New York) 10 Séminaire Lotharingien de Combinatoire 10 Algebras and Representation Theory 10 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Publications of the Research Institute for Mathematical Sciences, Kyoto University 9 Journal of the American Mathematical Society 8 Journal of Pure and Applied Algebra 7 Advances in Applied Mathematics 7 Annals of Combinatorics 6 Annales Henri Poincaré 5 International Journal of Modern Physics A 5 Inventiones Mathematicae 5 International Journal of Mathematics 5 St. Petersburg Mathematical Journal 5 Transformation Groups 5 Representation Theory 5 Algebraic & Geometric Topology 5 Journal of Physics A: Mathematical and Theoretical 4 Communications in Algebra 4 Journal of Statistical Physics 4 Physics Letters. B 4 Annales de l’Institut Fourier 4 SIAM Journal on Discrete Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Reviews in Mathematical Physics 3 The Annals of Probability 3 Journal of Computational and Applied Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Annalen 3 Topology and its Applications 3 Experimental Mathematics 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 Compositio Mathematica 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of the Mathematical Society of Japan 2 Memoirs of the American Mathematical Society 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 Discrete & Computational Geometry 2 Linear Algebra and its Applications 2 Proceedings of the National Academy of Sciences of the United States of America 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Vietnam Journal of Mathematics 2 Geometry & Topology 2 New Journal of Physics 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Journal of Algebra and its Applications 2 Quantum Topology 2 Bulletin of Mathematical Sciences 2 Forum of Mathematics, Sigma 1 Modern Physics Letters A 1 Analysis Mathematica 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 Theory of Probability and its Applications 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 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 Functional Analysis and its Applications ...and 39 more Serials all top 5 Cited in 45 Fields 349 Combinatorics (05-XX) 293 Nonassociative rings and algebras (17-XX) 258 Quantum theory (81-XX) 171 Algebraic geometry (14-XX) 132 Associative rings and algebras (16-XX) 131 Statistical mechanics, structure of matter (82-XX) 105 Group theory and generalizations (20-XX) 86 Special functions (33-XX) 56 Manifolds and cell complexes (57-XX) 41 Dynamical systems and ergodic theory (37-XX) 36 Number theory (11-XX) 35 Commutative algebra (13-XX) 26 Order, lattices, ordered algebraic structures (06-XX) 26 Global analysis, analysis on manifolds (58-XX) 20 Category theory; homological algebra (18-XX) 20 Partial differential equations (35-XX) 20 Probability theory and stochastic processes (60-XX) 19 Topological groups, Lie groups (22-XX) 19 Convex and discrete geometry (52-XX) 17 Difference and functional equations (39-XX) 14 \(K\)-theory (19-XX) 14 Ordinary differential equations (34-XX) 14 Functional analysis (46-XX) 12 Relativity and gravitational theory (83-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Differential geometry (53-XX) 10 Computer science (68-XX) 7 Several complex variables and analytic spaces (32-XX) 6 Algebraic topology (55-XX) 6 Mechanics of particles and systems (70-XX) 5 Operator theory (47-XX) 5 Geometry (51-XX) 5 Statistics (62-XX) 5 Information and communication theory, circuits (94-XX) 3 Functions of a complex variable (30-XX) 3 Integral equations (45-XX) 3 Numerical analysis (65-XX) 2 History and biography (01-XX) 2 Approximations and expansions (41-XX) 2 Abstract harmonic analysis (43-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year