Creation operators and algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{o}_3)$

Abstract

We define the elliptic quantum group $E_{\tau ,\eta }(s{o}_3)$ and the transfer matrix corresponding to its simplest highest weight representation. We use Bethe anstaz method to construct the creation operators as polynomials of the Lax matrix elements expressed through a recurrence relation. We give common eigenvectors and eigenvalues of the family of commuting transfer matrices.

13 pages

References in corpus (9)

• Quantum Inverse Scattering Method and Correlation Functions
• How Algebraic Bethe Ansatz works for integrable model
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• Elliptic quantum groups and Ruijsenaars models
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_n)$ and its applications
• Algebraic nested Bethe ansatz for the elliptic Ruijsenaars model
• Quasi-Hopf twistors for elliptic quantum groups

Cited by in corpus (3)

• Singularities of $n$-fold integrals of the Ising class and the theory of elliptic curves
• From Holonomy of the Ising Model Form Factors to n-Fold Integrals and the Theory of Elliptic Curve
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(A_2^{(2)})$