Abstract
We extend the Gervais-Neveu-Felderequation (GNFE) to the boundary case. Using the boundary GNFE, we give a definition of the boundary elliptic quantum group BE τ, η ( sl 2) The evaluation representation of the boundary elliptic quantum group BE τ, η ( sl 2) is presented. The Bethe ansatz for the boundary quantum group BE τ, η ( sl 2) is obtained. In a special case, the obtained Bethe ansatz is similar to the Bethe ansatz of the eight-vertex and the higher spin eight-vertex models with open boundary conditions.
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