Finite-dimensional irreducible modules for the three-point ${\mathfrak{sl}}_2$ loop algebra

Abstract

Recently Brian Hartwig and the second author found a presentation for the three-point $s{l}_2$ loop algebra by generators and relations. To obtain this presentation they defined a Lie algebra $⊠$ by generators and relations, and displayed an isomorphism from $⊠$ to the three-point $s{l}_2$ loop algebra. In this paper we describe the finite-dimensional irreducible $⊠$-modules from multiple points of view.

45 pages

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