Finite-dimensional irreducible modules of the racah algebra at characteristic zero

Hau Wen Huang, Sarah Bockting-Conrad

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Assume that F is an algebraically closed field with characteristic zero. The Racah algebra ℜ is the unital associative F-algebra defined by generators and relations in the following way. The generators are A, B, C, D and the relations assert that [A, B] = [B, C] = [C, A] = 2D and that each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. In this paper we discuss the finite-dimensional irreducible R-modules in detail and classify them up to isomorphism. To do this, we apply an infinite-dimensional R-module and its universal property. We additionally give the necessary and sufficient conditions for A, B, C to be diagonalizable on finite-dimensional irreducible R-modules.

Original languageEnglish
Article number018
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume16
DOIs
StatePublished - 2020

Keywords

  • Irreducible modules
  • Quadratic algebra
  • Racah algebra
  • Tridiagonal pairs
  • Universal property

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