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Algebraic Bethe ansatz for the elliptic quantum group $E_{τ,η}(sl_n)$ and its applications

We study the tensor product of the {\it higher spin representations} (see the definition in Sect. 2.2) of the elliptic quantum group $E_{τ,η}(sl_n)$. The transfer matrices associated with the $E_{τ,η}(sl_n)$-module are exactly diagonalized by the nested Bethe ansatz method. Some special cases of the construction give the exact solution for the $Z_n$ Belavin model and for the elliptic $A_{n-1}$ Ruijsenaars-Schneider model.