Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2) Original Research Article

To each representation of the elliptic quantum group 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 q-deformation of Hermiteʹs solution of the Lamé equation.