Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2)
Copyright policy )Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2)
To each representation of the elliptic quantum group $E_{��,��}(sl_2)$ 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�� equation.
18 pages, AMSLaTeX
- University of North Carolina at Chapel Hill United States
- University of North Carolina at Greensboro United States
spin chains, eigenvectors, Quantum groups (quantized enveloping algebras) and related deformations, integrable models, Hermite Lame equation solution, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), commuting transfer matrices, Exactly solvable models; Bethe ansatz, Quantum groups and related algebraic methods applied to problems in quantum theory, two-body Ruijsenaars operator
spin chains, eigenvectors, Quantum groups (quantized enveloping algebras) and related deformations, integrable models, Hermite Lame equation solution, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), commuting transfer matrices, Exactly solvable models; Bethe ansatz, Quantum groups and related algebraic methods applied to problems in quantum theory, two-body Ruijsenaars operator
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