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

TL;DR

This paper introduces an elliptic deformation of the affine Lie algebra sl_2, based on a novel RLL relation involving elliptic R-matrices, extending previous algebraic structures with conjectures on modules and vertex operators.

Contribution

It proposes a new elliptic quantum algebra for sl_2 using RLL relations with elliptic R-matrices, generalizing existing algebraic frameworks.

Findings

Reduces to a known algebra in the trigonometric limit.

Formulates conjectures on highest weight modules.

Discusses the physical interpretation of R*.

Abstract

An elliptic deformation of $\widehat{sl}_2$ is proposed. Our presentation of the algebra is based on the relation $RLL=LLR^*$, where $R$ and $R^*$ 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 $R^*$ is discussed.