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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134470Recently 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.45 pagesRepresentation TheoryRings and Algebras17B37; 05E35Finite-dimensional irreducible modules for the three-point $\mathfrak{sl}_2$ loop algebratext