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

Bo-yu Hou·Ryu Sasaki·Wen-Li Yang
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Abstract

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.

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Bo-yu Hou, Ryu Sasaki, Wen-Li Yang. 2003-07-06. Algebraic Bethe ansatz for the elliptic quantum group $E_{τ,η}(sl_n)$ and its applications. https://doi.org/10.1016/s0550-3213(03)00390-0

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