Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$

Abstract

To each representation of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$ 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 $q$-deformation of Hermite's solution of the Lamé equation.

18 pages, AMSLaTeX

References in corpus (1)

• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$

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