Tarasov, Vitaly Olegovich

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 Author ID: tarasov.vitaly-o Published as: Tarasov, V.; Tarasov, Vitaly; Tarasov, V. O.; Tarasov, Vitaly O.; Tarasov, Vitali Homepage: http://math.iupui.edu/people/vitaly-tarasov External Links: MGP
 Documents Indexed: 98 Publications since 1988, including 1 Book Co-Authors: 31 Co-Authors with 81 Joint Publications 879 Co-Co-Authors
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Co-Authors

 17 single-authored 53 Varchenko, Alexander Nikolaevich 25 Mukhin, Evgeny 7 Karolinsky, Eugene 7 Rimányi, Richárd 6 Stolin, Alexander 4 Eremenko, Alexandre Émmanuilovich 4 Nazarov, Maxim Leonidovich 3 Bikbaev, Ramil’ F. 3 Gabrielov, Andrei 2 Felder, Giovanni 2 Pakuliak, Stanislav Z. 2 Schechtman, Vadim 2 Uvarov, Filipp 1 Bibikov, P. N. 1 Faddeev, Lyudvig Dmitrievich 1 Felder, T. G. 1 Gorbounov, Vassily 1 Isaev, Alekseĭ Petrovich 1 Its, Alexander Rudolfovich 1 Khoroshkin, Sergey M. 1 Kirillov, Anatol N. 1 Laptev, Ari 1 Miwa, Tetsuji 1 Muzykin, Kolya 1 Nakayashiki, Atsushi 1 Sobolev, Alexander V. 1 Stolin, K. A. 1 Suslina, Tat’yana Aleksandrovna 1 Takeyama, Yoshihiro 1 Yafaev, Dimitri R. 1 Zinn-Justin, Paul
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Serials

 8 Letters in Mathematical Physics 5 Journal of Geometry and Physics 5 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 4 Advances in Mathematics 4 IMRN. International Mathematics Research Notices 3 Journal of Mathematical Sciences (New York) 3 St. Petersburg Mathematical Journal 2 Communications in Mathematical Physics 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Algebra i Analiz 2 Selecta Mathematica. New Series 2 Transformation Groups 2 Moscow Mathematical Journal 2 Journal of Physics A: Mathematical and Theoretical 1 International Journal of Modern Physics A 1 Houston Journal of Mathematics 1 Inverse Problems 1 Theoretical and Mathematical Physics 1 Reviews in Mathematical Physics 1 Acta Mathematica 1 Duke Mathematical Journal 1 Functional Analysis and its Applications 1 Gazette des Mathématiciens 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Soviet Mathematics 1 Mathematische Zeitschrift 1 Osaka Journal of Mathematics 1 Acta Applicandae Mathematicae 1 Journal of the American Mathematical Society 1 International Journal of Mathematics 1 Journal of Physics A: Mathematical and General 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Zapiski Nauchnykh Seminarov POMI 1 Mathematical Physics, Analysis and Geometry 1 Conformal Geometry and Dynamics 1 Annals of Mathematics. Second Series 1 Czechoslovak Journal of Physics 1 Central European Journal of Mathematics 1 Journal of Statistical Mechanics: Theory and Experiment 1 Journal of Mathematical Physics, Analysis, Geometry 1 Astérisque 1 Proceedings of the Steklov Institute of Mathematics 1 Functional Analysis and Other Mathematics 1 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 1 Confluentes Mathematici 1 Quantum Topology 1 European Journal of Mathematics
all top 5

Fields

 63 Nonassociative rings and algebras (17-XX) 42 Quantum theory (81-XX) 29 Statistical mechanics, structure of matter (82-XX) 17 Special functions (33-XX) 14 Partial differential equations (35-XX) 13 Algebraic geometry (14-XX) 12 Ordinary differential equations (34-XX) 11 Difference and functional equations (39-XX) 10 Several complex variables and analytic spaces (32-XX) 7 Dynamical systems and ergodic theory (37-XX) 7 Differential geometry (53-XX) 4 Associative rings and algebras (16-XX) 4 Algebraic topology (55-XX) 3 Functions of a complex variable (30-XX) 2 Commutative algebra (13-XX) 2 Group theory and generalizations (20-XX) 2 Topological groups, Lie groups (22-XX) 1 History and biography (01-XX) 1 $$K$$-theory (19-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX)

Citations contained in zbMATH Open

85 Publications have been cited 884 times in 478 Documents Cited by Year
Schubert calculus and representations of the general linear group. Zbl 1205.17026
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
Geometry of $$q$$-hypergeometric functions, quantum affine algebras and elliptic quantum groups. Zbl 0938.17012
Tarasov, V.; Varchenko, A.
1997
Geometric $$q$$-hypergeometric functions as a bridge between Yangians and quantum affine algebras. Zbl 0877.33013
Tarasov, V.; Varchenko, A.
1997
Differential equations compatible with KZ equations. Zbl 0984.35134
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000
Representations of Yangians with Gelfand-Zetlin bases. Zbl 0885.17009
Nazarov, Maxim; Tarasov, Vitaly
1998
The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Zbl 1213.14101
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2009
Yangians and Gelfand-Zetlin bases. Zbl 0929.17009
Nazarov, Maxim; Tarasov, Vitaly
1994
Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra. Zbl 1287.81063
Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A.
2013
Initial boundary value problem for the nonlinear Schrödinger equation. Zbl 0753.35090
Bikbaev, R. F.; Tarasov, V. O.
1991
Bispectral and $$(\mathfrak{gl}_N,\mathfrak{gl}_M)$$ dualities, discrete versus differential. Zbl 1142.82005
Mukhin, E.; Tarasov, V.; Varchenko, A.
2008
Bethe algebra of homogeneous $$XXX$$ Heisenberg model has simple spectrum. Zbl 1173.82006
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
Duality for Knizhnik-Zamolodchikov and dynamical equations. Zbl 1013.17006
Tarasov, V.; Varchenko, A.
2002
Trigonometric weight functions as $$K$$-theoretic stable envelope maps for the cotangent bundle of a flag variety. Zbl 1349.19002
Rimányi, R.; Tarasov, V.; Varchenko, A.
2015
Difference equations compatible with trigonometric KZ differential equations. Zbl 0971.39009
Tarasov, V.; Varchenko, A.
2000
On irreducibility of tensor products of Yangian modules associated with skew Young diagrams. Zbl 1027.17013
Nazarov, Maxim; Tarasov, Vitaly
2002
The integrable initial-boundary value problem on a semiline: Nonlinear Schrödinger and sine-Gordon equations. Zbl 0732.35089
Tarasov, V. O.
1991
Solutions of the elliptic qKZB equations and Bethe ansatz. I. Zbl 0884.65127
Felder, T. G.; Tarasov, V.; Varchenko, A.
1997
Combinatorial formulae for nested Bethe vectors. Zbl 1288.82024
Tarasov, Vitaly; Varchenko, Alexander
2013
Partial flag varieties, stable envelopes, and weight functions. Zbl 1361.14030
Rimányi, Richárd; Tarasov, Vitaly; Varchenko, Alexander
2015
Jackson integral representations for solutions of the quantized Knizhnik- Zamolodchikov equation. Zbl 0818.33012
Varchenko, A. N.; Tarasov, V. O.
1994
Selberg-type integrals associated with $$\mathfrak{sl}_3$$. Zbl 1055.33016
Tarasov, V.; Varchenko, A.
2003
Metrics with conic singularities and spherical polygons. Zbl 1405.30005
Eremenko, Alexandre; Gabrielov, Andrei; Tarasov, Vitaly
2014
On irreducibility of tensor products of Yangian modules. Zbl 0893.17011
Nazarov, Maxim; Tarasov, Vitaly
1998
A generalization of the Capelli identity. Zbl 1287.17026
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations. Zbl 1038.32500
Felder, G.; Tarasov, V.; Varchenko, A.
1999
Cyclic monodromy matrices for the $$R$$-matrix of the six-vertex model and the chiral Potts model with fixed spin boundary conditions. Zbl 0925.17018
Tarasov, Vitaly O.
1992
Metrics with four conic singularities and spherical quadrilaterals. Zbl 1343.30007
Eremenko, Alexandre; Gabrielov, Andrei; Tarasov, Vitaly
2016
KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians. Zbl 1269.82018
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2012
Off-shell Bethe vectors and Drinfeld currents. Zbl 1148.17010
Khoroshkin, S.; Pakuliak, S.; Tarasov, V.
2007
Elliptic and $$K$$-theoretic stable envelopes and Newton polytopes. Zbl 1452.55009
Rimányi, R.; Tarasov, V.; Varchenko, A.
2019
On reality property of Wronski maps. Zbl 1181.81065
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $$\mathfrak{gl}_{N}$$. Zbl 1219.82121
Mukhin, E.; Tarasov, V.; Varchenko, A.
2011
Bispectral and $$(\mathfrak{gl}_{N},\mathfrak{gl}_{M})$$ dualities. Zbl 1156.82005
Mukhin, Evgenii E.; Tarasov, Vitaly O.; Varchenko, Alexander N.
2006
Extended Joseph polynomials, quantized conformal blocks, and a $$q$$-Selberg type integral. Zbl 1254.22013
Rimányi, Richard; Tarasov, Vitaly O.; Varchenko, A.; Zinn-Justin, Paul
2012
Spaces of quasi-exponentials and representations of $$\mathfrak{gl}_N$$. Zbl 1142.81011
Mukhin, E.; Tarasov, V.; Varchenko, A.
2008
Cyclic monodromy matrices for $$sl(n)$$ trigonometric $$R$$-matrices. Zbl 0804.17011
Tarasov, Vitaly
1993
Generating operator of $$XXX$$ or Gaudin transfer matrices has quasi-exponential kernel. Zbl 1140.82015
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2007
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors. Zbl 0883.17021
Tarasov, V. O.; Varchenko, A. N.
1996
Spherical quadrilaterals with three non-integer angles. Zbl 1364.30048
Eremenko, A.; Gabrielov, A.; Tarasov, V.
2016
Bethe eigenvectors of higher transfer matrices. Zbl 1456.82301
Mukhin, E.; Tarasov, V.; Varchenko, A.
2006
Dynamical Yang-Baxter equations, quasi-Poisson homogeneous spaces, and quantization. Zbl 1102.17003
Karolinsky, E.; Muzykin, K.; Stolin, K. A.; Tarasov, V.
2005
Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety. Zbl 1294.82016
Tarasov, Vitaly; Varchenko, Alexander
2014
Bethe algebra of Gaudin model, Calogero-Moser space, and Cherednik algebra. Zbl 1304.82021
Mukhin, E.; Tarasov, V.; Varchenko, A.
2014
Irreducible highest weight modules and equivariant quantization. Zbl 1222.53093
Karolinsky, E.; Stolin, A.; Tarasov, V.
2007
Completeness of Bethe vectors and difference equations with regular singular points. Zbl 0860.17022
Tarasov, Vitaly; Varchenko, Alexander
1995
Spaces of quasi-exponentials and representations of the Yangian $$Y(\mathfrak{gl}_N)$$. Zbl 1365.17006
Mukhin, E.; Tarasov, V.; Varchenko, A.
2014
Bethe subalgebras of the group algebra of the symmetric group. Zbl 1276.82014
Mukhin, E.; Tarasov, V.; Varchenko, A.
2013
Dynamical differential equations compatible with rational qKZ equations. Zbl 1064.32012
Tarasov, V.; Varchenko, A.
2005
The boundary value problem for the nonlinear Schrödinger equation. Zbl 0693.35143
Tarasov, V. O.
1988
Boundary-value problem for nonlinear Schrödinger equation. Zbl 0696.35169
Bibikov, P. N.; Tarasov, V. O.
1989
Lower bounds for numbers of real solutions in problems of Schubert calculus. Zbl 1365.14070
Mukhin, Evgeny; Tarasov, Vitaly
2016
The determinant of a hypergeometric period matrix. Zbl 0968.32015
Markov, Y.; Tarasov, V.; Varchenko, A.
1998
How to regularize singular vectors and kill the dynamical Weyl group. Zbl 1046.17004
Styrkas, K.; Tarasov, V.; Varchenko, A.
2004
Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions. Zbl 1328.14082
Rimányi, R.; Tarasov, V.; Varchenko, A.
2014
On solutions of the KZ and qKZ equations at level zero. Zbl 0941.35089
Nakayashiki, A.; Pakuliak, S.; Tarasov, V.
1999
Bethe algebra of the $${\mathfrak {gl}}_{N+1}$$ Gaudin model and algebra of functions on the critical set of the master function. Zbl 1221.82038
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2011
Three sides of the geometric Langlands correspondence for $$\mathfrak{gl}_N$$ Gaudin model and Bethe vector averaging maps. Zbl 1260.82025
Mukhin, Eugene; Tarasov, Vitaly; Varchenko, Alexander
2012
Reality property of discrete Wronski map with imaginary step. Zbl 1299.81027
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2012
On separation of variables and completeness of the Bethe ansatz for quantum $$\mathfrak{gl}_N$$ Gaudin model. Zbl 1158.81336
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
Jackson integral representations of solutions of the quantized Knizhnik- Zamolodchikov equation. Zbl 0824.33012
Varchenko, A. N.; Tarasov, V. O.
1994
Identities between $$q$$-hypergeometric and hypergeometric integrals of different dimensions. Zbl 1113.33015
Tarasov, V.; Varchenko, A.
2005
Small elliptic quantum group $$e_{\tau,\gamma}(\mathfrak{sl}_N)$$. Zbl 0998.17018
Tarasov, V.; Varchenko, A.
2001
Solutions to the quantized Knizhnik-Zamolodchikov equation and the Bethe-Ansatz. Zbl 0902.39002
Tarasov, V.; Varchenko, A.
1995
Cohomology of a flag variety as a Bethe algebra. Zbl 1271.14072
Rimányi, R.; Schechtman, V.; Tarasov, V.; Varchenko, A.
2011
Higher Lamé equations and critical points of master functions. Zbl 1204.34122
Mukhin, E.; Tarasov, V.; Varchenko, A.
2007
On Bethe vectors for the $$XXZ$$ model at roots of unity. Zbl 1130.82009
Tarasov, V. O.
2002
A nonhomogeneous boundary value problem on a semiaxis and on an interval for the sine-Gordon equation. Zbl 0791.35120
Bikbaev, R. F.; Tarasov, V. O.
1991
An inhomogeneous boundary value problem on the semi-axis and on the closed interval for the sine-Gordon equation. Zbl 0762.35099
Bikbaev, R. F.; Tarasov, V. O.
1991
Equivariant quantization of Poisson homogeneous spaces and Kostant’s problem. Zbl 1368.17018
Karolinsky, E.; Stolin, A.; Tarasov, V.
2014
Completeness of the Bethe ansatz for the periodic isotropic Heisenberg model. Zbl 1397.82019
Tarasov, V.
2018
Fuchsian equations with three non-apparent singularities. Zbl 1397.34153
Eremenko, Alexandre; Tarasov, Vitaly
2018
Duality for Knizhnik-Zamolodchikov and dynamical operators. Zbl 07196492
Tarasov, Vitaly; Uvarov, Filipp
2020
Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel. Zbl 1171.82008
Mukhin, E.; Tarasov, V.; Varchenko, A.
2008
On a new form of Bethe ansatz equations and separation of variables in the $$\mathfrak{sl}_3$$ Gaudin model. Zbl 1154.82308
Mukhin, E.; Schechtman, V.; Tarasov, V.; Varchenko, A.
2007
Identities for hypergeometric integrals of different dimensions. Zbl 1088.33009
Tarasov, V.; Varchenko, A.
2005
Determinant formula for solutions of the quantum Knizhnik-Zamolodchikov equation associated with $$U_q (sl_n)$$ at $$|q|=1$$. Zbl 0963.33006
Miwa, Tetsuji; Takeyama, Yoshihiro; Tarasov, Vitaly
1999
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.
2016
Boundary-value problem for the nonlinear Schrödinger equation. Zbl 0725.35075
Tarasov, V. O.
1991
From dynamical to non-dynamical twists. Zbl 1097.17009
Karolinsky, E.; Stolin, A.; Tarasov, V.
2005
On conjectures of A. Eremenko and A. Gabrielov for quasi-exactly solvable quartic. Zbl 1269.81041
Mukhin, Evgeny; Tarasov, Vitaly
2013
Dynamical Yang-Baxter equation and quantization of certain Poisson brackets. Zbl 1103.17004
Karolinsky, Eugene; Stolin, Alexander; Tarasov, Vitaly
2005
Completeness of the hypergeometric solutions to the qKZ equation at level zero. Zbl 0964.39016
Tarasov, V.
2000
$$q$$-hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem. Zbl 1419.82020
Tarasov, Vitaly; Varchenko, Alexander
2019
Completeness of the Bethe ansatz for the periodic isotropic Heisenberg model. Zbl 1434.82030
Tarasov, V.
2018
Equivariant quantum differential equation, Stokes bases, and $$K$$-theory for a projective space. Zbl 1475.14111
Tarasov, Vitaly; Varchenko, Alexander
2021
Equivariant quantum differential equation, Stokes bases, and $$K$$-theory for a projective space. Zbl 1475.14111
Tarasov, Vitaly; Varchenko, Alexander
2021
Duality for Knizhnik-Zamolodchikov and dynamical operators. Zbl 07196492
Tarasov, Vitaly; Uvarov, Filipp
2020
Elliptic and $$K$$-theoretic stable envelopes and Newton polytopes. Zbl 1452.55009
Rimányi, R.; Tarasov, V.; Varchenko, A.
2019
$$q$$-hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem. Zbl 1419.82020
Tarasov, Vitaly; Varchenko, Alexander
2019
Completeness of the Bethe ansatz for the periodic isotropic Heisenberg model. Zbl 1397.82019
Tarasov, V.
2018
Fuchsian equations with three non-apparent singularities. Zbl 1397.34153
Eremenko, Alexandre; Tarasov, Vitaly
2018
Completeness of the Bethe ansatz for the periodic isotropic Heisenberg model. Zbl 1434.82030
Tarasov, V.
2018
Metrics with four conic singularities and spherical quadrilaterals. Zbl 1343.30007
Eremenko, Alexandre; Gabrielov, Andrei; Tarasov, Vitaly
2016
Spherical quadrilaterals with three non-integer angles. Zbl 1364.30048
Eremenko, A.; Gabrielov, A.; Tarasov, V.
2016
Lower bounds for numbers of real solutions in problems of Schubert calculus. Zbl 1365.14070
Mukhin, Evgeny; Tarasov, Vitaly
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.
2016
Trigonometric weight functions as $$K$$-theoretic stable envelope maps for the cotangent bundle of a flag variety. Zbl 1349.19002
Rimányi, R.; Tarasov, V.; Varchenko, A.
2015
Partial flag varieties, stable envelopes, and weight functions. Zbl 1361.14030
Rimányi, Richárd; Tarasov, Vitaly; Varchenko, Alexander
2015
Metrics with conic singularities and spherical polygons. Zbl 1405.30005
Eremenko, Alexandre; Gabrielov, Andrei; Tarasov, Vitaly
2014
Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety. Zbl 1294.82016
Tarasov, Vitaly; Varchenko, Alexander
2014
Bethe algebra of Gaudin model, Calogero-Moser space, and Cherednik algebra. Zbl 1304.82021
Mukhin, E.; Tarasov, V.; Varchenko, A.
2014
Spaces of quasi-exponentials and representations of the Yangian $$Y(\mathfrak{gl}_N)$$. Zbl 1365.17006
Mukhin, E.; Tarasov, V.; Varchenko, A.
2014
Cohomology classes of conormal bundles of Schubert varieties and Yangian weight functions. Zbl 1328.14082
Rimányi, R.; Tarasov, V.; Varchenko, A.
2014
Equivariant quantization of Poisson homogeneous spaces and Kostant’s problem. Zbl 1368.17018
Karolinsky, E.; Stolin, A.; Tarasov, V.
2014
Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra. Zbl 1287.81063
Gorbounov, V.; Rimányi, R.; Tarasov, V.; Varchenko, A.
2013
Combinatorial formulae for nested Bethe vectors. Zbl 1288.82024
Tarasov, Vitaly; Varchenko, Alexander
2013
Bethe subalgebras of the group algebra of the symmetric group. Zbl 1276.82014
Mukhin, E.; Tarasov, V.; Varchenko, A.
2013
On conjectures of A. Eremenko and A. Gabrielov for quasi-exactly solvable quartic. Zbl 1269.81041
Mukhin, Evgeny; Tarasov, Vitaly
2013
KZ characteristic variety as the zero set of classical Calogero-Moser Hamiltonians. Zbl 1269.82018
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2012
Extended Joseph polynomials, quantized conformal blocks, and a $$q$$-Selberg type integral. Zbl 1254.22013
Rimányi, Richard; Tarasov, Vitaly O.; Varchenko, A.; Zinn-Justin, Paul
2012
Three sides of the geometric Langlands correspondence for $$\mathfrak{gl}_N$$ Gaudin model and Bethe vector averaging maps. Zbl 1260.82025
Mukhin, Eugene; Tarasov, Vitaly; Varchenko, Alexander
2012
Reality property of discrete Wronski map with imaginary step. Zbl 1299.81027
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2012
Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $$\mathfrak{gl}_{N}$$. Zbl 1219.82121
Mukhin, E.; Tarasov, V.; Varchenko, A.
2011
Bethe algebra of the $${\mathfrak {gl}}_{N+1}$$ Gaudin model and algebra of functions on the critical set of the master function. Zbl 1221.82038
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2011
Cohomology of a flag variety as a Bethe algebra. Zbl 1271.14072
Rimányi, R.; Schechtman, V.; Tarasov, V.; Varchenko, A.
2011
Schubert calculus and representations of the general linear group. Zbl 1205.17026
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz. Zbl 1213.14101
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2009
Bethe algebra of homogeneous $$XXX$$ Heisenberg model has simple spectrum. Zbl 1173.82006
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
A generalization of the Capelli identity. Zbl 1287.17026
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
On reality property of Wronski maps. Zbl 1181.81065
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
On separation of variables and completeness of the Bethe ansatz for quantum $$\mathfrak{gl}_N$$ Gaudin model. Zbl 1158.81336
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009
Bispectral and $$(\mathfrak{gl}_N,\mathfrak{gl}_M)$$ dualities, discrete versus differential. Zbl 1142.82005
Mukhin, E.; Tarasov, V.; Varchenko, A.
2008
Spaces of quasi-exponentials and representations of $$\mathfrak{gl}_N$$. Zbl 1142.81011
Mukhin, E.; Tarasov, V.; Varchenko, A.
2008
Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel. Zbl 1171.82008
Mukhin, E.; Tarasov, V.; Varchenko, A.
2008
Off-shell Bethe vectors and Drinfeld currents. Zbl 1148.17010
Khoroshkin, S.; Pakuliak, S.; Tarasov, V.
2007
Generating operator of $$XXX$$ or Gaudin transfer matrices has quasi-exponential kernel. Zbl 1140.82015
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2007
Irreducible highest weight modules and equivariant quantization. Zbl 1222.53093
Karolinsky, E.; Stolin, A.; Tarasov, V.
2007
Higher Lamé equations and critical points of master functions. Zbl 1204.34122
Mukhin, E.; Tarasov, V.; Varchenko, A.
2007
On a new form of Bethe ansatz equations and separation of variables in the $$\mathfrak{sl}_3$$ Gaudin model. Zbl 1154.82308
Mukhin, E.; Schechtman, V.; Tarasov, V.; Varchenko, A.
2007
Bispectral and $$(\mathfrak{gl}_{N},\mathfrak{gl}_{M})$$ dualities. Zbl 1156.82005
Mukhin, Evgenii E.; Tarasov, Vitaly O.; Varchenko, Alexander N.
2006
Bethe eigenvectors of higher transfer matrices. Zbl 1456.82301
Mukhin, E.; Tarasov, V.; Varchenko, A.
2006
Dynamical Yang-Baxter equations, quasi-Poisson homogeneous spaces, and quantization. Zbl 1102.17003
Karolinsky, E.; Muzykin, K.; Stolin, K. A.; Tarasov, V.
2005
Dynamical differential equations compatible with rational qKZ equations. Zbl 1064.32012
Tarasov, V.; Varchenko, A.
2005
Identities between $$q$$-hypergeometric and hypergeometric integrals of different dimensions. Zbl 1113.33015
Tarasov, V.; Varchenko, A.
2005
Identities for hypergeometric integrals of different dimensions. Zbl 1088.33009
Tarasov, V.; Varchenko, A.
2005
From dynamical to non-dynamical twists. Zbl 1097.17009
Karolinsky, E.; Stolin, A.; Tarasov, V.
2005
Dynamical Yang-Baxter equation and quantization of certain Poisson brackets. Zbl 1103.17004
Karolinsky, Eugene; Stolin, Alexander; Tarasov, Vitaly
2005
How to regularize singular vectors and kill the dynamical Weyl group. Zbl 1046.17004
Styrkas, K.; Tarasov, V.; Varchenko, A.
2004
Selberg-type integrals associated with $$\mathfrak{sl}_3$$. Zbl 1055.33016
Tarasov, V.; Varchenko, A.
2003
Duality for Knizhnik-Zamolodchikov and dynamical equations. Zbl 1013.17006
Tarasov, V.; Varchenko, A.
2002
On irreducibility of tensor products of Yangian modules associated with skew Young diagrams. Zbl 1027.17013
Nazarov, Maxim; Tarasov, Vitaly
2002
On Bethe vectors for the $$XXZ$$ model at roots of unity. Zbl 1130.82009
Tarasov, V. O.
2002
Small elliptic quantum group $$e_{\tau,\gamma}(\mathfrak{sl}_N)$$. Zbl 0998.17018
Tarasov, V.; Varchenko, A.
2001
Differential equations compatible with KZ equations. Zbl 0984.35134
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000
Difference equations compatible with trigonometric KZ differential equations. Zbl 0971.39009
Tarasov, V.; Varchenko, A.
2000
Completeness of the hypergeometric solutions to the qKZ equation at level zero. Zbl 0964.39016
Tarasov, V.
2000
Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations. Zbl 1038.32500
Felder, G.; Tarasov, V.; Varchenko, A.
1999
On solutions of the KZ and qKZ equations at level zero. Zbl 0941.35089
Nakayashiki, A.; Pakuliak, S.; Tarasov, V.
1999
Determinant formula for solutions of the quantum Knizhnik-Zamolodchikov equation associated with $$U_q (sl_n)$$ at $$|q|=1$$. Zbl 0963.33006
Miwa, Tetsuji; Takeyama, Yoshihiro; Tarasov, Vitaly
1999
Representations of Yangians with Gelfand-Zetlin bases. Zbl 0885.17009
Nazarov, Maxim; Tarasov, Vitaly
1998
On irreducibility of tensor products of Yangian modules. Zbl 0893.17011
Nazarov, Maxim; Tarasov, Vitaly
1998
The determinant of a hypergeometric period matrix. Zbl 0968.32015
Markov, Y.; Tarasov, V.; Varchenko, A.
1998
Geometry of $$q$$-hypergeometric functions, quantum affine algebras and elliptic quantum groups. Zbl 0938.17012
Tarasov, V.; Varchenko, A.
1997
Geometric $$q$$-hypergeometric functions as a bridge between Yangians and quantum affine algebras. Zbl 0877.33013
Tarasov, V.; Varchenko, A.
1997
Solutions of the elliptic qKZB equations and Bethe ansatz. I. Zbl 0884.65127
Felder, T. G.; Tarasov, V.; Varchenko, A.
1997
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors. Zbl 0883.17021
Tarasov, V. O.; Varchenko, A. N.
1996
Completeness of Bethe vectors and difference equations with regular singular points. Zbl 0860.17022
Tarasov, Vitaly; Varchenko, Alexander
1995
Solutions to the quantized Knizhnik-Zamolodchikov equation and the Bethe-Ansatz. Zbl 0902.39002
Tarasov, V.; Varchenko, A.
1995
Yangians and Gelfand-Zetlin bases. Zbl 0929.17009
Nazarov, Maxim; Tarasov, Vitaly
1994
Jackson integral representations for solutions of the quantized Knizhnik- Zamolodchikov equation. Zbl 0818.33012
Varchenko, A. N.; Tarasov, V. O.
1994
Jackson integral representations of solutions of the quantized Knizhnik- Zamolodchikov equation. Zbl 0824.33012
Varchenko, A. N.; Tarasov, V. O.
1994
Cyclic monodromy matrices for $$sl(n)$$ trigonometric $$R$$-matrices. Zbl 0804.17011
Tarasov, Vitaly
1993
Cyclic monodromy matrices for the $$R$$-matrix of the six-vertex model and the chiral Potts model with fixed spin boundary conditions. Zbl 0925.17018
Tarasov, Vitaly O.
1992
Initial boundary value problem for the nonlinear Schrödinger equation. Zbl 0753.35090
Bikbaev, R. F.; Tarasov, V. O.
1991
The integrable initial-boundary value problem on a semiline: Nonlinear Schrödinger and sine-Gordon equations. Zbl 0732.35089
Tarasov, V. O.
1991
A nonhomogeneous boundary value problem on a semiaxis and on an interval for the sine-Gordon equation. Zbl 0791.35120
Bikbaev, R. F.; Tarasov, V. O.
1991
An inhomogeneous boundary value problem on the semi-axis and on the closed interval for the sine-Gordon equation. Zbl 0762.35099
Bikbaev, R. F.; Tarasov, V. O.
1991
Boundary-value problem for the nonlinear Schrödinger equation. Zbl 0725.35075
Tarasov, V. O.
1991
Boundary-value problem for nonlinear Schrödinger equation. Zbl 0696.35169
Bibikov, P. N.; Tarasov, V. O.
1989
The boundary value problem for the nonlinear Schrödinger equation. Zbl 0693.35143
Tarasov, V. O.
1988
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Cited by 459 Authors

 48 Varchenko, Alexander Nikolaevich 40 Tarasov, Vitaly Olegovich 26 Mukhin, Evgeny 19 Rimányi, Richárd 13 Mudrov, Andrey I. 12 Molev, Alexander I. 11 Khoroshkin, Sergey M. 11 Morozov, Alexei Yurievich 11 Pakuliak, Stanislav Z. 10 Ragoucy, Eric 9 Eremenko, Alexandre Émmanuilovich 9 Mironov, Andrei D. 9 Nazarov, Maxim Leonidovich 8 Khabibullin, Ismagil Talgatovich 8 Young, Charles A. S. 7 Gabrielov, Andrei 7 Slavnov, Nikita A. 7 Zabrodin, Anton V. 7 Zotov, Andrei V. 6 Feĭgin, Boris L’vovich 6 Ito, Masahiko 6 Koroteev, Peter 6 Vicedo, Benoît 6 Zenkevich, Yegor 6 Zinn-Justin, Paul 5 Awata, Hidetoshi 5 Felder, Giovanni 5 Kanno, Hiroaki 5 Lu, Kang 5 Rybnikov, Leonid Grigor’evich 5 Sottile, Frank 5 Toledano Laredo, Valerio 5 Warnaar, S. Ole 5 Weber, Andrzej 4 Caudrelier, Vincent 4 Crampé, Nicolas 4 Gromov, Nikolay A. 4 Levkovich-Maslyuk, Fedor 4 Nepomechie, Rafael I. 4 Niccoli, Giuliano 4 Ogievetsky, Oleg V. 4 Ol’shanskiĭ, Grigoriĭ Iosifovich 4 Purbhoo, Kevin 4 Regelskis, Vidas 4 Smirnov, Andrey V. 4 Stokman, Jasper V. 4 Volin, Dmytro 4 Zeitlin, Anton M. 3 Bikbaev, Ramil’ F. 3 Biondini, Gino 3 Boutet de Monvel, Anne Marie 3 Corrigan, Edward 3 Derkachëv, Sergeĭ Èduardovich 3 Etingof, Pavel Il’ich 3 Fehér, László M. 3 Finkelberg, Michael Vladlenovich 3 Galleas, Wellington 3 Gorskiĭ, Aleksandr Sergeevich 3 Hein, Nickolas 3 Hernandez, David 3 Ignat’ev, Mikhail Yur’evich 3 Jimbo, Michio 3 Korff, Christian 3 Kozlowski, Karol Kajetan 3 Kumar, Shrawan 3 Leurent, Sebastien 3 Liashyk, A. N. 3 Mimachi, Katsuhisa 3 Poulain D’Andecy, Loïc 3 Pusztai, Béla Gábor 3 Su, Changjian 3 Sun, Yi 3 Tsuboi, Zengo 3 Wendlandt, Curtis 3 Zhong, Changlong 2 Aganagic, Mina 2 Aggarwal, Amol 2 Alexandrov, Alexander Sergeevich 2 Aminov, G. A. 2 Aomoto, Kazuhiko 2 Appel, Andrea 2 Avan, Jean 2 Basu-Mallick, Bireswar 2 Baxter, Rodney J. 2 Belkale, Prakash 2 Belliard, Samuel 2 Bowcock, Peter 2 Bulycheva, Kseniya 2 Cao, Junpeng 2 Chalykh, Oleg A. 2 Chen, Heng-Yu 2 Chervov, Alexander Viktorovich 2 Conley, Charles H. 2 Deift, Percy A. 2 del Campo, Abraham Martín 2 Donin, Joseph 2 Dorey, Patrick E. 2 Falqui, Gregorio 2 Finkel, Federico 2 Forrester, Peter J. ...and 359 more Authors
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Cited in 112 Serials

 35 Communications in Mathematical Physics 33 Journal of High Energy Physics 32 Advances in Mathematics 29 Letters in Mathematical Physics 26 Nuclear Physics. B 23 Theoretical and Mathematical Physics 22 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 17 Journal of Algebra 16 Journal of Mathematical Physics 11 Journal of Geometry and Physics 11 Selecta Mathematica. New Series 10 Duke Mathematical Journal 8 Transactions of the American Mathematical Society 7 Transformation Groups 6 Journal of Mathematical Sciences (New York) 6 St. Petersburg Mathematical Journal 5 Reviews in Mathematical Physics 5 Advances in Applied Mathematics 5 Algebras and Representation Theory 5 Journal of Physics A: Mathematical and Theoretical 5 Arnold Mathematical Journal 4 Inventiones Mathematicae 4 Journal of Combinatorial Theory. Series A 4 Mathematische Annalen 4 Proceedings of the American Mathematical Society 4 Journal of Statistical Mechanics: Theory and Experiment 3 Mathematical Notes 3 Annales de l’Institut Fourier 3 Compositio Mathematica 3 Illinois Journal of Mathematics 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Journal of the American Mathematical Society 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Algebraic Combinatorics 3 Mathematical Physics, Analysis and Geometry 3 Annales Henri Poincaré 2 International Journal of Modern Physics A 2 Journal of Mathematical Analysis and Applications 2 Journal of Statistical Physics 2 Physics Letters. A 2 Physics Letters. B 2 Acta Mathematica 2 Functional Analysis and its Applications 2 Journal of Pure and Applied Algebra 2 Mathematische Zeitschrift 2 Studies in Applied Mathematics 2 Transactions of the Moscow Mathematical Society 2 International Journal of Mathematics 2 Linear Algebra and its Applications 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Experimental Mathematics 2 Journal of Algebraic Geometry 2 The New York Journal of Mathematics 2 Representation Theory 2 The Ramanujan Journal 2 Communications in Contemporary Mathematics 2 Journal of Nonlinear Mathematical Physics 2 Computational Methods and Function Theory 2 Central European Journal of Mathematics 2 Mathematics 1 Applicable Analysis 1 Communications in Algebra 1 Computers & Mathematics with Applications 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Publications Mathématiques 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Results in Mathematics 1 Tokyo Journal of Mathematics 1 European Journal of Combinatorics 1 Probability Theory and Related Fields 1 Discrete & Computational Geometry 1 Applied Mathematics Letters 1 Mathematical and Computer Modelling 1 Formal Aspects of Computing 1 Geometric and Functional Analysis. GAFA 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Journal of Knot Theory and its Ramifications 1 Journal of Nonlinear Science 1 Applied Categorical Structures 1 Integral Transforms and Special Functions 1 Izvestiya: Mathematics 1 Vietnam Journal of Mathematics 1 Conformal Geometry and Dynamics 1 Geometry & Topology 1 Regular and Chaotic Dynamics 1 Journal of the European Mathematical Society (JEMS) 1 Czechoslovak Journal of Physics 1 Foundations of Computational Mathematics 1 Advanced Nonlinear Studies 1 Milan Journal of Mathematics 1 Journal of the Institute of Mathematics of Jussieu 1 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 International Journal of Geometric Methods in Modern Physics ...and 12 more Serials
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Cited in 46 Fields

 192 Quantum theory (81-XX) 188 Nonassociative rings and algebras (17-XX) 109 Statistical mechanics, structure of matter (82-XX) 86 Algebraic geometry (14-XX) 59 Special functions (33-XX) 58 Partial differential equations (35-XX) 51 Associative rings and algebras (16-XX) 43 Dynamical systems and ergodic theory (37-XX) 37 Ordinary differential equations (34-XX) 34 Combinatorics (05-XX) 30 Group theory and generalizations (20-XX) 27 Differential geometry (53-XX) 22 Several complex variables and analytic spaces (32-XX) 21 Difference and functional equations (39-XX) 17 Topological groups, Lie groups (22-XX) 16 Global analysis, analysis on manifolds (58-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 14 Algebraic topology (55-XX) 13 $$K$$-theory (19-XX) 13 Functions of a complex variable (30-XX) 11 Probability theory and stochastic processes (60-XX) 6 Number theory (11-XX) 6 Mechanics of particles and systems (70-XX) 6 Relativity and gravitational theory (83-XX) 5 Commutative algebra (13-XX) 5 Manifolds and cell complexes (57-XX) 4 Field theory and polynomials (12-XX) 4 Operator theory (47-XX) 4 Numerical analysis (65-XX) 3 Category theory; homological algebra (18-XX) 3 Geometry (51-XX) 2 Real functions (26-XX) 2 Potential theory (31-XX) 2 Functional analysis (46-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 General algebraic systems (08-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Information and communication theory, circuits (94-XX)