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Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau,\eta}(sl_2)$
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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.
Forward citations
Cited by 2 Pith papers
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On correlation functions of the open XYZ spin 1/2 chain with boundary fields related by a constraint
Exact multiple sums and multiple integrals are derived for elementary correlation-function building blocks of the open XYZ spin-1/2 chain with one constraint on its six boundary fields.
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Long-range to the Rescue of Yang-Baxter II
A long-range Bethe ansatz produces four-magnon eigenstates, recursively built from three-magnon data, for the one-loop spin chain of a marginally deformed Z2 orbifold of N=4 SYM.
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