A classification of finite-dimensional irreducible representations of the Yangian $Y(gl_2)$ has been obtained. In several papers (joint with A. N. Varchenko, as well as G. Felder and Ya. Markov) $q$-hypergeometric solutions of the difference Knizhnik–Zamolodchikov equations has been studied. In a few joint papers with M. L. Nazarov we studied finite-dimensional irreducible representations of the Yangians $Y(gl_N)$ and Gelfand–Zetlin bases of these representations.
Biography
Graduated from Physics Department, Leningrad University in mathematical physics in 1982. Ph.D — 1985, Leningrad Branch of V. A. Steklov Mathematical Institute.
Main publications:
V. Tarasov. The integrable initial-boundary value problem on a semiline: nonlinear Schroedinger and sine-Gordon equations // Inverse problems, 1991, 7(3), 435–450.
V. Tarasov, A. Varchenko. Completeness of Bethe vectors and difference equations with regular singular points // Int. Math. Res. Not. 1995, 13, 637–669.
V. Tarasov, A. Varchenko. Geometry of $q$-hypergeometric functions, quantum affine algebras and elliptic quantum groups // Asterisque, 1997, 246, 1–135.
M. Nazarov, V. Tarasov. Representations of Yangians with Gelfand–Zetlin bases // J. Reine Angew. Math., 1998, 496, 181–212.
A. G. Pronko, V. O. Tarasov, “Polynomial structure in determinants for Izergin–Korepin partition function”, Zap. Nauchn. Sem. POMI, 520 (2023), 227–238; J. Math. Sci. (N. Y.), 284:5 (2024), 726–734
2020
3.
Vitaly Tarasov, Filipp Uvarov, “Duality for Knizhnik–Zamolodchikov and Dynamical Operators”, SIGMA, 16 (2020), 035, 10 pp.
Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “KZ characteristic variety as the zero set of classical Calogero–Moser Hamiltonians”, SIGMA, 8 (2012), 072, 11 pp.
A. N. Varchenko, R. Rimányi, V. O. Tarasov, V. V. Schechtman, “Cohomology of a flag variety as a Bethe algebra”, Funktsional. Anal. i Prilozhen., 45:4 (2011), 16–31; Funct. Anal. Appl., 45:4 (2011), 252–264
E. Mukhin, V. Tarasov, A. Varchenko, “Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\frak{gl}_N$”, Algebra i Analiz, 22:3 (2010), 177–190; St. Petersburg Math. J., 22:3 (2011), 463–472
Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel”, SIGMA, 3 (2007), 060, 31 pp.
E. E. Mukhin, V. Schechtman, V. O. Tarasov, A. N. Varchenko, “On a New Form of Bethe Ansatz Equations and Separation of Variables in the $\mathfrak{sl}_3$ Gaudin model”, Trudy Mat. Inst. Steklova, 258 (2007), 162–184; Proc. Steklov Inst. Math., 258 (2007), 155–177
V. O. Tarasov, “On Bethe vectors for the $XXZ$ model at roots of unity”, Zap. Nauchn. Sem. POMI, 291 (2002), 251–262; J. Math. Sci. (N. Y.), 125:2 (2005), 242–248
V. O. Tarasov, “On solutions of Bethe equations for the $XXZ$ model”, Zap. Nauchn. Sem. POMI, 291 (2002), 245–250; J. Math. Sci. (N. Y.), 125:2 (2005), 239–241
2001
15.
V. O. Tarasov, A. N. Varchenko, “Small elliptic quantum group $e_{\tau,\gamma}(\mathfrak{sl}_N)$”, Mosc. Math. J., 1:2 (2001), 243–286
V. O. Tarasov, “Combinatorial Identities Related to Representations of $U_q(\widetilde{\mathfrak{gl}_2})$”, Trudy Mat. Inst. Steklova, 226 (1999), 152–162; Proc. Steklov Inst. Math., 226 (1999), 138–148
A. N. Varchenko, V. O. Tarasov, “Jackson integral representations for solutions of the Knizhnik–Zamolodchikov quantum equation”, Algebra i Analiz, 6:2 (1994), 90–137; St. Petersburg Math. J., 6:2 (1995), 275–313
V. O. Tarasov, “On solutions to the twisted Yang–Baxter equation”, Zap. Nauchn. Sem. POMI, 215 (1994), 301–308; J. Math. Sci. (New York), 85:1 (1997), 1752–1757
R. F. Bikbaev, V. O. Tarasov, “An inhomogeneous boundary value problem on the semi-axis and on a segment for the sine-Gordon equation”, Algebra i Analiz, 3:4 (1991), 78–92; St. Petersburg Math. J., 3:4 (1992), 775–789
P. N. Bibikov, V. O. Tarasov, “Boundary-value problem for nonlinear Schrödinger equation”, TMF, 79:3 (1989), 334–346; Theoret. and Math. Phys., 79:3 (1989), 570–579
V. O. Tarasov, “Irreducible monodromy matrices for the $R$ matrix of the $XXZ$ model and local lattice quantum Hamiltonians”, TMF, 63:2 (1985), 175–196; Theoret. and Math. Phys., 63:2 (1985), 440–454
V. O. Tarasov, “Irreducible monodromy matrices for the $R$-matrix of the $XXZ$-model, and lattice local quantum Hamiltonians”, Dokl. Akad. Nauk SSSR, 278:5 (1984), 1102–1105
25.
V. O. Tarasov, “Local Hamiltonians for integrable quantum models on a lattice. II”, TMF, 61:3 (1984), 387–392; Theoret. and Math. Phys., 61:3 (1984), 1211–1215
V. O. Tarasov, “Structure of quantum L operators for the R matrix of the XXZ model”, TMF, 61:2 (1984), 163–173; Theoret. and Math. Phys., 61:2 (1984), 1065–1072
V. O. Tarasov, L. A. Takhtadzhyan, L. D. Faddeev, “Local Hamiltonians for integrable quantum models on a lattice”, TMF, 57:2 (1983), 163–181; Theoret. and Math. Phys., 57:2 (1983), 1059–1073
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