Representation of the boundary elliptic quantum group BEτ,η(sl2) and the Bethe ansatz Original Research Article

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 BEτ,η(sl2) The evaluation representation of the boundary elliptic quantum group BEτ,η(sl2) is presented. The Bethe ansatz for the boundary quantum group BEτ,η(sl2) 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.