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Elliptic Quantum Groups and Ruijsenaars Models

Giovanni Felder, Alexander N. Varchenko

Published Aug 14, 2021• 0 citations
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Abstract

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groups Eτ,η(glN). The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.

DOI
10.17615/574h-f292

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To each representation of the elliptic quantum group Eτ,η(sl2)E_{\tau,\eta}(sl_2)Eτ,η​(sl2​) is associated a family of commuting transfer matrices. We give common eigenvectors by a version of the algebraic Bethe ansatz method. Special cases of this construction give eigenvectors for IRF models, for the eight-vertex model and for the two-body Ruijsenaars operator. The latter is a qqq-deformation of Hermite's solution of the Lam\'e equation.