Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sln) and its applications Original Research Article

We study the tensor product of the higher spin representations (see the definition in Section 2.2) of the elliptic quantum group Eτ,η(sln). The transfer matrices associated with the Eτ,η(sln)-module are exactly diagonalized by the nested Bethe ansatz method. Some special cases of the construction give the exact solution for the Zn Belavin model and for the elliptic An−1 Ruijsenaars–Schneider model.