dorsal/arxiv
View SchemaAlgebraic Bethe ansatz for the elliptic quantum group $E_{\tau,\eta}(sl_2)$
| Authors | Giovanni Felder, Alexander Varchenko |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9605024 |
| URL | https://arxiv.org/abs/q-alg/9605024 |
| DOI | 10.1016/S0550-3213(96)00461-0 |
Abstract
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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"date_modified": "2026-03-02T18:01:27.603000Z",
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"abstract": "To each representation of the elliptic quantum group $E_{\\tau,\\eta}(sl_2)$ is\nassociated a family of commuting transfer matrices. We give common eigenvectors\nby a version of the algebraic Bethe ansatz method. Special cases of this\nconstruction give eigenvectors for IRF models, for the eight-vertex model and\nfor the two-body Ruijsenaars operator. The latter is a $q$-deformation of\nHermite\u0027s solution of the Lam\\\u0027e equation.",
"arxiv_id": "q-alg/9605024",
"authors": [
"Giovanni Felder",
"Alexander Varchenko"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1016/S0550-3213(96)00461-0",
"title": "Algebraic Bethe ansatz for the elliptic quantum group $E_{\\tau,\\eta}(sl_2)$",
"url": "https://arxiv.org/abs/q-alg/9605024"
},
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