91 citations · 871 across the 69 of their papers we have counts for
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On solutions of the KZ and qKZ equations at level zero
A. Nakayashiki, S. Pakuliak, V. Tarasov
We discuss relations between different formulae for solutions of the Knizhnik-Zamolodchikov differential and the quantum Knizhnik-Zamolodchikov difference equations at level 0 and…
Bilinear Identity for q-Hypergeometric Integrals
Vitaly Tarasov
We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation f…
Monodromy of solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations
Giovanni Felder, Vitaly Tarasov, Alexander Varchenko
The elliptic quantum Knizhnik-Zamolodchikov-Bernard (qKZB) difference equations associated to the elliptic quantum group is a system of difference equations with va…
Geometry of q-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups
Vitaly Tarasov, Alexander Varchenko
The trigonometric quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the quantum group is a system of linear difference equations with values in a…
Solutions of the elliptic qKZB equations and Bethe ansatz I
Giovanni Felder, Alexander Varchenko, Vitaly Tarasov
We give an integral representation for solutions of the elliptic quantum Knizhnik-Zamolodchikov-Bernard difference equations, in the case of sl(2). The result is based on a geometr…
Geometry of q-Hypergeometric Functions as a Bridge between Yangians and Quantum Affine Algebras
Vitaly Tarasov, Alexander Varchenko
The rational quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the Lie algebra is a system of linear difference equations with values in a tensor prod…
Bases of Bethe Vectors and Difference Equations with Regular Singular Points
Vitaly Tarasov, Alexander Varchenko
We prove that Bethe vectors generically form a base in a tensor product of irreducible heighest weight -modules or -modules. We apply this result to difference equ…
Representations of Yangians with Gelfand-Zetlin Bases
Maxim Nazarov, Vitaly Tarasov
We study certain family of finite-dimensional modules over the Yangian . The algebra comes equipped with a distinguished maximal commutative subalgebra …