Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$ and its applications

Abstract

We study the tensor product of the {\it higher spin representations} (see the definition in Sect. 2.2) of the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$. The transfer matrices associated with the $E_{\tau ,\eta }(s{l}_n)$-module are exactly diagonalized by the nested Bethe ansatz method. Some special cases of the construction give the exact solution for the $Z_n$ Belavin model and for the elliptic $A_{n-1}$ Ruijsenaars-Schneider model.

23 pages, latex file, to appear in Nucl. Phys. B

References in corpus (1)

• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism

Cited by in corpus (17)

• Exact solution of $Z_n$ Belavin model with open boundary condition
• Exact solution of the $A_{n-1}^{(1)}$ trigonometric vertex model with non-diagonal open boundaries
• $Z_n$ elliptic Gaudin model with open boundaries
• Non-diagonal solutions of the reflection equation for the trigonometric $A_{n-1}^{(1)}$ vertex model
• Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Scalar products of the open XYZ chain with non-diagonal boundary terms
• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
• Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
• Creation operators and algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{o}_3)$
• Elliptic quantum groups and Baxter relations
• Construction of the Bethe State for the $E_{\tau ,\eta }(s{o}_3)$ Elliptic Quantum Group
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(A_2^{(2)})$
• Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms
• On the solutions of the $Z_n$-Belavin model with arbitrary number of sites