167 citations · 1.9k across the 134 of their papers we have counts for
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Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB and Macdonald-Ruijsenaars equations
K. Styrkas, A. Varchenko
The resonance relations are identities between coordinates of functions with values in tensor products of representations of the quantum group Uq(sl2). We show that the space of hy…
A generalization of the Capelli identity
E. Mukhin, V. Tarasov, A. Varchenko
We prove a generalization of the Capelli identity. As an application we obtain an isomorphism of the Bethe subalgebras actions under the (gl(N),gl(M)) duality.
Bispectral and (gl_N, gl_M) Dualities, Discrete Versus Differential
E. Mukhin, V. Tarasov, A. Varchenko
Let be a space of quasi-polynomials in of dimension . The regularized fundamental differential operator of…
Bethe eigenvectors of higher transfer matrices
E. Mukhin, V. Tarasov, A. Varchenko
We consider the XXX-type and Gaudin quantum integrable models associated with the Lie algebra . The models are defined on a tensor product irreducible -modules. For eac…
Quasi-polynomials and the Bethe Ansatz
E Mukhin, A Varchenko
We study solutions of the Bethe Ansatz equation related to the trigonometric Gaudin model associated to a simple Lie algebra g and a tensor product of irreducible finite-dimensiona…
Determinants of the hypergeometric period matrices of an arrangement and its dual
D. Mukherjee, A. Varchenko
We fix three natural numbers , such that , and introduce the notion of two dual arrangements of hyperplanes. One of the arrangements is an arrangement of hype…
Higher Lame Equations and Critical Points of Master Functions
E. Mukhin, V. Tarasov, A. Varchenko
Under certain conditions, we give an estimate from above on the number of differential equations of order with prescribed regular singular points, prescribed exponents at sin…