An elliptic quantum algebra for ${\widehat{sl}}_2$

Abstract

An elliptic deformation of ${\widehat{sl}}_2$ is proposed. Our presentation of the algebra is based on the relation $RLL=LL{R}^{\ast }$, where $R$ and $R^{\ast }$ are eight-vertex $R$-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest weight modules and vertex operators are formulated, and the physical interpretation of $R^{\ast }$ is discussed.

(Final version for publication.)