Finite-dimensional irreducible modules of the universal Askey–Wilson algebra at roots of unity

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Abstract

Let F denote an algebraically closed field and assume that q∈F is a primitive dth root of unity with d≠1,2,4. The universal Askey–Wilson algebra △q is a unital associative F-algebra defined by generators and relations. The generators are A,B,C and the relations assert that each of [Formula presented] [Formula presented] commutes with A,B,C. We show that every finite-dimensional irreducible △q-module is of dimension less than or equal to {difdis odd;d/2ifdis even. Moreover we provide an example to show that the bound is tight.

Original languageEnglish
Pages (from-to)12-29
Number of pages18
JournalJournal of Algebra
Volume569
DOIs
StatePublished - 1 Mar 2021

Keywords

  • Askey–Wilson algebras
  • Chebyshev polynomials
  • q-Racah sequences

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