Construction of the Bethe State for the $E_{\tau ,\eta }(s{o}_3)$ Elliptic Quantum Group

Abstract

Elliptic quantum groups can be associated to solutions of the star-triangle relation of statistical mechanics. In this paper, we consider the particular case of the $E_{\tau ,\eta }(s{o}_3)$ elliptic quantum group. In the context of algebraic Bethe ansatz, we construct the corresponding Bethe creation operator for the transfer matrix defined in an arbitrary representation of $E_{\tau ,\eta }(s{o}_3)$.

This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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• Quantum Inverse Scattering Method and Correlation Functions
• How Algebraic Bethe Ansatz works for integrable model
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
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Cited by in corpus (1)

• Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations