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arXiv:hep-th/0303077 · Nuclear Physics B

Algebraic Bethe ansatz for the elliptic quantum group E,(sl) and its applications

B.Y. Hou, Ryu Sasaki B, Wen‐Li Yang

Published Jun 2, 2003• 19 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(03)00390-0

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Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2)E_{\tau,\eta}(sl_2)Eτ,η​(sl2​)
To each representation of the elliptic quantum group Eτ,η(sl2)E_{\tau,\eta}(sl_2)Eτ,η​(sl2​) 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 qqq-deformation of Hermite's solution of the Lam\'e equation.