An elliptic quantum algebra for \widehats1₂ 2

1994/03/31 by Omar Foda, Kenji Iohara, K. Iohara +8 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #hep-th #math.QA

paper · pdf · doi:10.1007/bf00750668

published as Lett.Math.Phys. 32 (1994) 259-268 · (Final version for publication.)

arxiv created 1994/05/12 · openalex publication_date 1994/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

An elliptic deformation of \widehatsl₂ 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.

Citations

• Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. II. Equivalence to a generalized ice-type lattice model

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