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

References in corpus (6)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• The structure of quotients of the Onsager algebra by closed ideals
• sl(N) Onsager's Algebra and Integrability
• Nonlinear holomorphic supersymmetry, Dolan-Grady relations and Onsager algebra
• The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model
• The Universal Central Extension of the Three-point sl_2 Loop Algebra

Cited by in corpus (13)

• The Drinfel'd polynomial of a tridiagonal pair
• The alternating central extension of the $q$-Onsager algebra
• Towards a classification of the tridiagonal pairs
• How to sharpen a tridiagonal pair
• A classification of sharp tridiagonal pairs
• Sharp tridiagonal pairs
• Mock Tridiagonal Systems
• Tridiagonal pairs of $q$-Racah type
• The structure of a tridiagonal pair
• Tridiagonal pairs and the q-tetrahedron algebra
• On the shape of a tridiagonal pair
• Double Lowering Operators on Polynomial
• Lie algebras with S3 or S4-action, and generalized Malcev algebras