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

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

1994-03-17

arxiv.org/abs/hep-th/9403094v3

Lett.Math.Phys. 32 (1994) 259-268

Physics

High Energy Physics

High Energy Physics - Theory

(Final version for publication.)

Scientific paper

10.1007/BF00750668

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.

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