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Kirillov, Anatol N.

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Author ID: kirillov.anatol-n Recent zbMATH articles by "Kirillov, Anatol N."
Published as: Kirillov, A. N.; Kirillov, Anatol N.; Kirillov, Anatoli
Homepage: http://www.kurims.kyoto-u.ac.jp/~kirillov/
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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

Publications by Year

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 0852.05078
Fomin, Sergey; Kirillov, Anatol N.
91
1996
q-Weyl group and a multiplicative formula for universal R-matrices. Zbl 0723.17014
Kirillov, A. N.; Reshetikhin, N.
86
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.
73
1989
Quadratic algebras, Dunkl elements, and Schubert calculus. Zbl 0940.05070
Fomin, Sergey; Kirillov, Anatol N.
64
1999
Dilogarithm identities. Zbl 0894.11052
Kirillov, Anatol N.
55
1995
The Bethe Ansatz and the combinatorics of Young tableaux. Zbl 0639.20029
Kirillov, A. N.; Reshetikhin, N. Yu.
53
1988
A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013
Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark
41
2002
Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060
Fomin, Sergey; Kirillov, Anatol N.
41
1996
Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025
Kirillov, A. N.; Reshetikhin, N. Yu.
33
1986
Introduction to tropical combinatorics. Zbl 0989.05127
Kirillov, 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 0900.16047
Kirillov, A. N.; Reshetikhin, N. Yu.
29
1987
Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007
Kirillov, A. N.; Berenstein, A. D.
27
1995
The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027
Kirillov, A. N.; Reshetikhin, N. Yu.
25
1986
Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024
Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu.
24
1986
Affine Hecke algebras and raising operators for Macdonald polynomials. Zbl 0939.05090
Kirillov, Anatol N.; Noumi, Masatoshi
24
1998
Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028
Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu.
23
1988
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
21
1999
Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014
Kirillov, A. N.
20
1987
Torus knot and minimal model. Zbl 1094.81550
Hikami, Kazuhiro; Kirillov, Anatol N.
19
2003
An invitation to the generalized saturation conjecture. Zbl 1077.05098
Kirillov, Anatol N.
17
2004
Ubiquity of Kostka polynomials. Zbl 0982.05105
Kirillov, Anatol N.
17
2001
\(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015
Kirillov, A. N.; Noumi, M.
17
1999
Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029
Kirillov, A. N.; Reshetikhin, N. Yu.
17
1986
Notes on Schubert, Grothendieck and key polynomials. Zbl 1334.05176
Kirillov, Anatol N.
16
2016
Reduced words and plane partitions. Zbl 0882.05010
Fomin, Sergey; Kirillov, Anatol N.
16
1997
A generalization of the Kostka-Foulkes polynomials. Zbl 0995.05146
Kirillov, Anatol N.; Shimozono, Mark
15
2002
New combinatorial formula for modified Hall-Littlewood polynomials. Zbl 0956.05101
Kirillov, Anatol N.
14
2000
Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules. Zbl 0811.17032
Begin, 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 0637.16007
Kirillov, A. N.; Reshetikhin, N. Yu.
12
1987
Noncommutative algebras related with Schubert calculus on Coxeter groups. Zbl 1106.05103
Kirillov, Anatol N.; Maeno, Toshiaki
12
2004
Completeness of states of the generalized Heisenberg magnet. Zbl 0613.58014
Kirillov, A. N.
11
1987
Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008
Kirillov, 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 1348.05213
Kirillov, Anatol N.
10
2016
Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0958.05137
Kirillov, Anatol N.; Maeno, Toshiaki
10
2000
Skew Young diagram method in spectral decomposition of integrable lattice models. Zbl 0887.17008
Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki
9
1997
On some algebraic and combinatorial properties of Dunkl elements. Zbl 1260.13030
Kirillov, Anatol N.
9
2012
On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009
Kirillov, A. N.
9
1988
Completeness of states of the generalized Heisenberg magnet. Zbl 0538.58016
Kirillov, A. N.
9
1984
Norms of bound states. Zbl 0637.47004
Kirillov, A. N.; Korepin, V. E.
8
1988
Combinatorics and geometry of higher level Weyl modules. Zbl 1129.22011
Feigin, B.; Kirillov, A. N.; Loktev, S.
8
2007
Construction of double Grothendieck polynomials of classical types using idcoxeter algebras. Zbl 1364.05081
Kirillov, Anatol N.; Naruse, Hiroshi
8
2017
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
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.
7
1993
On some quadratic algebras. Zbl 0966.05080
Kirillov, A. N.
7
2000
Completeness of Bethe’s states for the generalized \(XXZ\) model. Zbl 1001.82516
Kirillov, Anatol N.; Liskova, Nadejda A.
6
1997
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
5
2005
Unimodality of generalized Gaussian coefficients. Zbl 0768.05002
Kirillov, Anatol N.
5
1992
Universal exponential solution of the Yang-Baxter equation. Zbl 0867.17009
Fomin, Sergey; Kirillov, Anatol N.
5
1996
Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. Zbl 1225.16023
Kirillov, Anatol N.; Maeno, Toshiaki
5
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
Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106
Kirillov, A. N.; Smirnov, F. A.
5
1989
Generalized Umemura polynomials. Zbl 1080.33019
Kirillov, Anatol N.; Taneda, Makoto
4
2002
The Clebsch-Gordan quantum coefficients. Zbl 0722.17006
Kirillov, A. N.
4
1991
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
Skew divided difference operators and Schubert polynomials. Zbl 1146.05053
Kirillov, Anatol N.
4
2007
Quantum Schubert polynomials and quantum Schur functions. Zbl 1040.05029
Kirillov, Anatol N.
4
1999
Singular solutions to the Bethe ansatz equations and rigged configurations. Zbl 1302.82034
Kirillov, Anatol N.; Sakamoto, Reiho
4
2014
Generalized Umemura polynomials and the Hirota-Miwa equation. Zbl 1029.34084
Kirillov, Anatol N.; Taneda, Makoto
3
2002
Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006
Kirillov, Anatol N.; Maeno, Toshiaki
3
2005
Zeta-function of the mondromy for complete intersection singularities. Zbl 0597.14016
Kirillov, A. N.
3
1981
A combinatorial formula for the associated Legendre functions of integer degree. Zbl 0941.33007
van Diejen, J. F.; Kirillov, A. N.
3
2000
Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties. Zbl 1233.05213
Kirillov, 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 0925.17003
Kirillov, Anatol N.
3
1992
Lutz filtration of formal groups. Zbl 0337.14032
Bashmakov, M. I.; Kirillov, A. N.
3
1975
On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063
Kirillov, Anatol N.; Maeno, Toshiaki
3
2005
The quantum Clebsch-Gordan coefficients. Zbl 0684.17003
Kirillov, A. N.
3
1988
Valance bond solid in quasicrystals. Zbl 0717.60118
Kirillov, A. N.; Korepin, V. E.
3
1990
Equilibrium and control in the biocommunity species composition preservation problem. Zbl 1377.93030
Ivanova, A. S.; Kirillov, A. N.
2
2017
Hypergeometric generating function of \(L\)-function, Slater’s identities, and quantum invariant. Zbl 1136.11308
Hikami, K.; Kirillov, A. N.
2
2006
T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model. Zbl 0644.35084
Kirillov, A. N.
2
1988
Entanglement in valence-bond-solid states on symmetric graphs. Zbl 1193.82049
Katsura, Hosho; Kawashima, Naoki; Kirillov, Anatol N.; Korepin, Vladimir E.; Tanaka, Shu
2
2010
Domino tableaux, Schützenberger involution, and the symmetric group action. Zbl 0965.05094
Berenstein, Arkady; Kirillov, Anatol N.
2
2000
Determinantal formulas for zonal spherical functions on hyperboloids. Zbl 0983.43007
van Diejen, J. F.; Kirillov, A. N.
2
2001
Clebsch-Gordan and Racah-Wigner coefficients for \(U_q(SU(1,1))\). Zbl 0925.17007
Liskova, N. A.; Kirillov, A. N.
2
1992
Some remarks on Nepomechie-Wang eigenstates for spin 1/2 XXX model. Zbl 1336.81040
Kirillov, Anatol N.; Sakamoto, Reiho
2
2015
Various representations of the generalized Kostka polynomials. Zbl 0921.05067
Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark
2
1999
Norm pairing in a two-dimensional local field. Zbl 0566.12006
Vostokov, S. V.; Kirillov, A. N.
2
1985
The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032
Kirillov, A. N.; Reshetikhin, N. Yu.
2
1985
Lagrange identity and Hook formula. Zbl 0689.05010
Kirillov, A. N.
2
1989
Affine nil-Hecke algebras and braided differential structure on affine Weyl groups. Zbl 1278.16036
Kirillov, Anatol N.; Maeno, Toshiaki
2
2012
Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015
Kirillov, Anatol N.; Sakamoto, Reiho
1
2016
Lagrange’s identity and the Hook formula. Zbl 0780.05004
Kirillov, A. N.
1
1989
Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019
Kirillov, Anatol N.; Sakamoto, Reiho
1
2009
Classification of the string solutions of Bethe equations in an XXZ model of arbitrary spin. Zbl 0644.35085
Kirillov, A. N.; Reshetikhin, N. Yu.
1
1988
On some properties of Robinson-Schensted correspondence. Zbl 0778.05085
Kirillov, Anatoli
1
1991
Paths and Kostka-Macdonald polynomials. Zbl 1230.05287
Kirillov, Anatol N.; Sakamoto, Reiho
1
2009
Cauchy identities for universal Schubert polynomials. Zbl 1063.05134
Kirillov, A. N.
1
2001
\(t\)-deformations of quantum Schubert polynomials. Zbl 1108.14307
Kirillov, Anatol N.
1
2000
T-invariance, CPT-invariance and local commutativity of the quantum model \((ch\phi)_ 2\). Zbl 0606.35069
Kirillov, A. N.
1
1985
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.
1
2016
Combinatorics of Young tableaux and configurations. Zbl 0990.05137
Kirillov, A. N.
1
2001
Rigged configurations and Catalan, stretched parabolic Kostka numbers and polynomials: polynomiality, unimodality and log-concavity. Zbl 1409.05210
Kirillov, Anatol N.
1
2018
Commutative formal groups. Zbl 0402.14018
Kirillov, A. N.
1
1979
Braided differential structure on Weyl groups, quadratic algebras, and elliptic functions. Zbl 1222.47051
Kirillov, Anatol N.; Maeno, Toshiaki
1
2008
Lutz filtration of formal groups. Zbl 0342.14021
Bashmakov, M. I.; Kirillov, A. N.
1
1977
Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0951.14507
Kirillov, Anatol N.; Maeno, Toshiaki
1
1999
On \(Q\)-deformations of Postnikov-Shapiro algebras. Zbl 1385.05086
Kirillov, Anatol N.; Nenashev, Gleb
1
2017
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
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
8
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.
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 1348.05213
Kirillov, Anatol N.
10
2016
Bethe’s quantum numbers and rigged configurations. Zbl 1332.82015
Kirillov, Anatol N.; Sakamoto, Reiho
1
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.
1
2016
Some remarks on Nepomechie-Wang eigenstates for spin 1/2 XXX model. Zbl 1336.81040
Kirillov, Anatol N.; Sakamoto, Reiho
2
2015
Bethe subalgebras in Hecke algebra and Gaudin models. Zbl 1292.81077
Isaev, Alexey P.; Kirillov, Anatol N.
6
2014
Singular solutions to the Bethe ansatz equations and rigged configurations. Zbl 1302.82034
Kirillov, Anatol N.; Sakamoto, Reiho
4
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
2
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
Nichols-Woronowicz model of coinvariant algebra of complex reflection groups. Zbl 1225.16023
Kirillov, Anatol N.; Maeno, Toshiaki
5
2010
Entanglement in valence-bond-solid states on symmetric graphs. Zbl 1193.82049
Katsura, Hosho; Kawashima, Naoki; Kirillov, Anatol N.; Korepin, Vladimir E.; Tanaka, Shu
2
2010
Relationships between two approaches: rigged configurations and 10-eliminations. Zbl 1251.37019
Kirillov, Anatol N.; Sakamoto, Reiho
1
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.
8
2007
Skew divided difference operators and Schubert polynomials. Zbl 1146.05053
Kirillov, Anatol N.
4
2007
Hypergeometric generating function of \(L\)-function, Slater’s identities, and quantum invariant. Zbl 1136.11308
Hikami, K.; Kirillov, A. N.
2
2006
A note on quantization operators on Nichols algebra model for Schubert calculus on Weyl groups. Zbl 1104.14021
Kirillov, Anatol N.; Maeno, Toshiaki
5
2005
Exterior differential algebras and flat connections on Weyl groups. Zbl 1101.58006
Kirillov, Anatol N.; Maeno, Toshiaki
3
2005
On some noncommutative algebras related to \(K\)-theory of flag varieties. I. Zbl 1101.14063
Kirillov, Anatol N.; Maeno, Toshiaki
3
2005
An invitation to the generalized saturation conjecture. Zbl 1077.05098
Kirillov, Anatol N.
17
2004
Noncommutative algebras related with Schubert calculus on Coxeter groups. Zbl 1106.05103
Kirillov, Anatol N.; Maeno, Toshiaki
12
2004
Torus knot and minimal model. Zbl 1094.81550
Hikami, Kazuhiro; Kirillov, Anatol N.
19
2003
A bijection between Littlewood-Richardson tableaux and rigged configurations. Zbl 0986.05013
Kirillov, Anatol N.; Schilling, Anne; Shimozono, Mark
41
2002
A generalization of the Kostka-Foulkes polynomials. Zbl 0995.05146
Kirillov, Anatol N.; Shimozono, Mark
15
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.
30
2001
Ubiquity of Kostka polynomials. Zbl 0982.05105
Kirillov, Anatol N.
17
2001
Determinantal formulas for zonal spherical functions on hyperboloids. Zbl 0983.43007
van Diejen, J. F.; Kirillov, A. N.
2
2001
Cauchy identities for universal Schubert polynomials. Zbl 1063.05134
Kirillov, A. N.
1
2001
Combinatorics of Young tableaux and configurations. Zbl 0990.05137
Kirillov, A. N.
1
2001
New combinatorial formula for modified Hall-Littlewood polynomials. Zbl 0956.05101
Kirillov, Anatol N.
14
2000
Quantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula. Zbl 0958.05137
Kirillov, Anatol N.; Maeno, Toshiaki
10
2000
On some quadratic algebras. Zbl 0966.05080
Kirillov, A. N.
7
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
Domino tableaux, Schützenberger involution, and the symmetric group action. Zbl 0965.05094
Berenstein, Arkady; Kirillov, Anatol N.
2
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.
64
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
21
1999
\(q\)-difference raising operators for Macdonald polynomials and the integrality of transition coefficients. Zbl 0947.33015
Kirillov, A. N.; Noumi, M.
17
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 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
24
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.
16
1997
Skew Young diagram method in spectral decomposition of integrable lattice models. Zbl 0887.17008
Kirillov, Anatol N.; Kuniba, Atsuo; Nakanishi, Tomoki
9
1997
Completeness of Bethe’s states for the generalized \(XXZ\) model. Zbl 1001.82516
Kirillov, Anatol N.; Liskova, Nadejda A.
6
1997
The Yang-Baxter equation, symmetric functions, and Schubert polynomials. Zbl 0852.05078
Fomin, Sergey; Kirillov, Anatol N.
91
1996
Combinatorial \(B_ n\)-analogues of Schubert polynomials. Zbl 0871.05060
Fomin, Sergey; Kirillov, Anatol N.
41
1996
Universal exponential solution of the Yang-Baxter equation. Zbl 0867.17009
Fomin, Sergey; Kirillov, Anatol N.
5
1996
Dilogarithm identities. Zbl 0894.11052
Kirillov, Anatol N.
55
1995
Groups generated by involutions, Gelfand-Tsetlin patterns, and combinatorics of Young tableaux. Zbl 0848.20007
Kirillov, A. N.; Berenstein, A. D.
27
1995
Dilogarithm identities, partitions, and spectra in conformal field theory. Zbl 0831.33008
Kirillov, A. N.
10
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.
13
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.
7
1993
Unimodality of generalized Gaussian coefficients. Zbl 0768.05002
Kirillov, 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 0925.17003
Kirillov, Anatol N.
3
1992
Clebsch-Gordan and Racah-Wigner coefficients for \(U_q(SU(1,1))\). Zbl 0925.17007
Liskova, N. A.; Kirillov, A. N.
2
1992
The Clebsch-Gordan quantum coefficients. Zbl 0722.17006
Kirillov, A. N.
4
1991
On some properties of Robinson-Schensted correspondence. Zbl 0778.05085
Kirillov, Anatoli
1
1991
q-Weyl group and a multiplicative formula for universal R-matrices. Zbl 0723.17014
Kirillov, A. N.; Reshetikhin, N.
86
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.
73
1989
Form-factors in the SU(2)-invariant Thirring model. Zbl 0692.35106
Kirillov, A. N.; Smirnov, F. A.
5
1989
Lagrange identity and Hook formula. Zbl 0689.05010
Kirillov, A. N.
2
1989
Lagrange’s identity and the Hook formula. Zbl 0780.05004
Kirillov, A. N.
1
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.
53
1988
Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0639.20028
Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu.
23
1988
On the Kostka-Green-Foulkes polynomials and Clebsch-Gordan numbers. Zbl 0695.22009
Kirillov, A. N.
9
1988
Norms of bound states. Zbl 0637.47004
Kirillov, A. N.; Korepin, V. E.
8
1988
Multiplicity of weights in irreducible tensor representations of a complete linear superalgebra. Zbl 0675.17013
Kirillov, A. N.; Reshetikhin, N. Yu.
6
1988
The quantum Clebsch-Gordan coefficients. Zbl 0684.17003
Kirillov, A. N.
3
1988
T-invariance, CPT-invariance, and local commutativity for the quantum \((\cosh\phi)_ 2\)-model. Zbl 0644.35084
Kirillov, A. N.
2
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.
1
1988
Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras. Zbl 0900.16047
Kirillov, A. N.; Reshetikhin, N. Yu.
29
1987
Identities for the Rogers dilogarithm function connected with simple Lie algebras. Zbl 0685.33014
Kirillov, A. N.
20
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.
12
1987
Completeness of states of the generalized Heisenberg magnet. Zbl 0613.58014
Kirillov, A. N.
11
1987
Bethe Ansatz and combinatorics of the Young tableaux. Zbl 0617.20025
Kirillov, A. N.; Reshetikhin, N. Yu.
33
1986
The Yangians, Bethe Ansatz and combinatorics. Zbl 0643.20027
Kirillov, A. N.; Reshetikhin, N. Yu.
25
1986
Combinatorics, Bethe Ansatz, and representations of the symmetric group. Zbl 0617.20024
Kerov, S. V.; Kirillov, A. N.; Reshetikhin, N. Yu.
24
1986
Exact solution of the Heisenberg XXZ model of spin s. Zbl 0612.35029
Kirillov, A. N.; Reshetikhin, N. Yu.
17
1986
Norm pairing in a two-dimensional local field. Zbl 0566.12006
Vostokov, S. V.; Kirillov, A. N.
2
1985
The exact solution of the Heisenberg XXZ-model of the spin S. Zbl 0586.35032
Kirillov, A. N.; Reshetikhin, N. Yu.
2
1985
T-invariance, CPT-invariance and local commutativity of the quantum model \((ch\phi)_ 2\). Zbl 0606.35069
Kirillov, A. N.
1
1985
Completeness of states of the generalized Heisenberg magnet. Zbl 0538.58016
Kirillov, A. N.
9
1984
Zeta-function of the mondromy for complete intersection singularities. Zbl 0597.14016
Kirillov, A. N.
3
1981
Commutative formal groups. Zbl 0402.14018
Kirillov, A. N.
1
1979
Lutz filtration of formal groups. Zbl 0342.14021
Bashmakov, M. I.; Kirillov, A. N.
1
1977
Lutz filtration of formal groups. Zbl 0337.14032
Bashmakov, M. I.; Kirillov, A. N.
3
1975
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