11 citations · 25 across the 10 of their papers we have counts for
8 papers · 1 filter
Multiple orthogonal polynomials and a counterexample to Gaudin Bethe Ansatz Conjecture
E. Mukhin, A. Varchenko
Jacobi polynomials are polynomials whose zeros form the unique solution of the Bethe Ansatz equation associated with two sl_2 irreducible modules. We study sequences of r polynomia…
Selberg Integrals
Alexander Varchenko
The paper is written for Kluwer's Encyclopaedia of Mathematics.
Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model
Alexander Varchenko
We show that the Shapovalov norm of a Bethe vector in the Gaudin model is equal to the Hessian of the logarithm of the corresponding master function at the corresponding isolated c…
Norm of a Bethe Vector and the Hessian of the Master Function
Evgeny Mukhin, Alexander Varchenko
We show that the Bethe vectors are non-zero vectors in the sl_{r+1} Gaudin model. Moreover, we show that the norm of a Bethe vector is equal to the Hessian of the corresponding mas…
Miura Opers and Critical Points of Master Functions
Evgeny Mukhin, Alexander Varchenko
Critical points of a master function associated to a simple Lie algebra \g come in families called the populations [MV1]. We prove that a population is isomorphic to the flag varie…
Identities between q-hypergeometric and hypergeometric integrals of different dimensions
V. Tarasov, A. Varchenko
Given complex numbers and nonnegative integers , such that , for any we define an -dimensional Barnes type q-hy…