A. Varchenko

activity

19932023

most citedGeometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation

167 citations · 1.9k across the 134 of their papers we have counts for

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Showing 2006 · math.QAShow all

5 papers · 2 filters

math.QA2006

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…

math.QA2006★ 1 cited

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.

math.QA2006★ 3 cited

Bispectral and (gl_N, gl_M) Dualities, Discrete Versus Differential

E. Mukhin, V. Tarasov, A. Varchenko

Let $V =< x^{λ_{i}} p_{ij} (x), i = 1, ..., n, j = 1, ..., N_{i} >$ be a space of quasi-polynomials in $x$ of dimension $N = N_{1} + ... + N_{n}$ . The regularized fundamental differential operator of…

math.QA2006★ 52 cited

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 $g l_{N}$ . The models are defined on a tensor product irreducible $g l_{N}$ -modules. For eac…

math.QA2006★ 27 cited

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…