Abstract
To each representation of the elliptic quantum group E τ, η ( sl 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.
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