The Tetrahedron algebra and its finite-dimensional irreducible modules

Abstract

Recently Terwilliger and the present author found a presentation for the three-point ${\mathfrak{sl}}_2$ loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra $⊠$ by generators and relations and displayed an isomorphism from $⊠$ to the three-point ${\mathfrak{sl}}_2$ loop algebra. In this paper we classify the finite-dimensional irreducible $⊠$-modules.

18 pages

References in corpus (1)

• The structure of quotients of the Onsager algebra by closed ideals

Cited by in corpus (1)

• On the shape of a tridiagonal pair