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An elliptic quantum algebra for\(\widehat{s1}_2 \) 2

Dedicated to the memory of Ansgar Schnizer

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Abstract

An elliptic deformation of\(\widehat{s1}_2 \) is proposed. Our presentation of the algebra is based on the relationRLL = LLR *, whereR andR * are eight-vertexR-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 ofR * is discussed.

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Foda, O., Iohara, K., Jimbo, M. et al. An elliptic quantum algebra for\(\widehat{s1}_2 \) 2 . Lett Math Phys 32, 259–268 (1994). https://doi.org/10.1007/BF00750668

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