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

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