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

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

2003-03-10

arxiv.org/abs/hep-th/0303077v3

Nucl.Phys. B663 (2003) 467-486

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, latex file, to appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(03)00390-0

We study the tensor product of the {\it higher spin representations} (see the definition in Sect. 2.2) of the elliptic quantum group $E_{\tau,\eta}(sl_n)$. The transfer matrices associated with the $E_{\tau,\eta}(sl_n)$-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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