167 citations · 1.9k across the 134 of their papers we have counts for
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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…
Combinatorics of rational functions and Poincare-Birkhoff-Witt expansions of the canonical U(n-)-valued differential form
R. Rimanyi, L. Stevens, A. Varchenko
We study the canonical U(n-)-valued differential form, whose projections to different Kac-Moody algebras are key ingredients of the hypergeometric integral solutions of KZ-type dif…
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…
Finite order invariants for -torus knots and the curve
Svetlana Tyurina, Alexander Varchenko
We describe the algebra of finite order invariants on the set of all -torus knots.
Discrete Miura Opers and Solutions of the Bethe Ansatz Equations
Evgeny Mukhin, Alexander Varchenko
Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra come in families called the populations. We prove that a population is isomorphic to the…