11 citations · 23 across the 8 of their papers we have counts for
8 papers
Poincare-Birkhoff-Witt expansions of the canonical elliptic differential form
G. Felder, R. Rimanyi, A. Varchenko
We study the canonical U(\n)-valued elliptic differential form, whose projections to different Kac-Moody algebras are key ingredients of the hypergeometric integral solutions of el…
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…
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…