Construction of the Bethe State for the $E_{τ,η}(so_3)$ Elliptic Quantum Group

Mathematics – Quantum Algebra

Scientific paper

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This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portuga

Scientific paper

10.3842/SIGMA.2007.004

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 $E_{\tau,\eta}(so_3)$ 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 $E_{\tau,\eta}(so_3)$.

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