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

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

2007-07-16

arxiv.org/abs/0707.2313v1

Mathematics

Representation Theory

45 pages

Scientific paper

Recently Brian Hartwig and the second author found a presentation for the three-point $sl_2$ loop algebra by generators and relations. To obtain this presentation they defined a Lie algebra $\boxtimes$ by generators and relations, and displayed an isomorphism from $\boxtimes$ to the three-point $sl_2$ loop algebra. In this paper we describe the finite-dimensional irreducible $\boxtimes$-modules from multiple points of view.

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