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

Giovanni Felder; Alexander Varchenko

doi:10.1016/s0550-3213(96)00461-0

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arXiv · q-alg/9605024

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

Giovanni Felder·Alexander Varchenko

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Abstract

To each representation of the elliptic quantum group $E_{τ,η}(sl_2)$ 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 Lamé equation.

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Giovanni Felder, Alexander Varchenko. 1996-05-15. Algebraic Bethe ansatz for the elliptic quantum group $E_{τ,η}(sl_2)$. https://doi.org/10.1016/s0550-3213(96)00461-0

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