Algebraic Bethe ansatz for the elliptic quantum group $E_{τ,η}(sl_2)$

Details Algebraic Bethe ansatz for the elliptic quantum group $E_{τ,η}(sl_2)$ Algebraic Bethe ansatz for the elliptic quantum group $E_{τ,η}(sl_2)$

1996-05-15

arxiv.org/abs/q-alg/9605024v1

Mathematics

Quantum Algebra

18 pages, AMSLaTeX

Scientific paper

10.1016/S0550-3213(96)00461-0

To each representation of the elliptic quantum group $E_{\tau,\eta}(sl_2)$ is associated a family of commuting transfer matrices. We give common eigenvectors by a version of the algebraic Bethe ansatz method. Special cases of this construction give eigenvectors for IRF models, for the eight-vertex model and for the two-body Ruijsenaars operator. The latter is a $q$-deformation of Hermite's solution of the Lam\'e equation.

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