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Three formulas for eigenfunctions of integrable Schroedinger operators
Giovanni Felder, Alexander Varchenko
We give three formulas for meromorphic eigenfunctions (scattering states) of Sutherland's integrable N-body Schroedinger operators and their generalizations. The first is an explic…
Remarks on the structure constants of the Verlinde algebra associated to
Giovanni Felder, Alexander Varchenko
The structure constants of the Verlinde algebra as functions of either vanish or can be expressed after a change of variable as the weight function of a…
Integral representation of solutions of the elliptic Knizhnik--Zamolodchikov--Bernard equations
Giovanni Felder, Alexander Varchenko
We give an integral representation of solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equations for arbitrary simple Lie algebras. If the level is a positive integer, we o…
On algebraic equations satisfied by hypergeometric correlators in WZW models. II
Boris Feigin, Vadim Schechtman, Alexander Varchenko
We give an explicit description of "bundles of conformal blocks" in Wess-Zumino-Witten models of Conformal field theory and prove that integral representations of Knizhnik-Zamolodc…
Asymptotic Solutions to the Quantized Knizhnik-Zamolodchikov Equation and Bethe Vectors
Vitaly Tarasov, Alexander Varchenko
Asymptotic solutions to the quantized Knizhnik-Zamolodchikov equation associated with are constructed. The leading term of an asymptotic solution is the Bethe vec…
Quasiclassical asymptotics of solutions to the KZ equations
Nicolai Reshetikhin, Alexander Varchenko
The quasiclassical asymptotics of the Knizhnik-Zamolodchikov system is studied. Solutions to this system in this limit are related naturally to Bethe vectors in the Gaudin model of…
Critical Points of the Product of Powers of Linear Functions and Families of Bases of Singular Vectors
Alexander Varchenko
The quasiclassical asymptotics of the Knizhnik-Zamolodchikov equation with values in the tensor product of sl(2)- representations are considered. The first term of asymptotics is a…
Jackson Integral Representations for Solutions to the Quantized Knizhnik-Zamolodchikov Equation
Vitaly Tarasov, Alexander Varchenko
The quantized Knizhnik-Zamolodchikov equations associated with the trigonometric R-matrix or the rational R-matrix of the A-type are considered. Jackson integral representations fo…