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.
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.
