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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 language | English |
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Pages (from-to) | 12-29 |

Number of pages | 18 |

Journal | Journal of Algebra |

Volume | 569 |

DOIs | |

State | Published - 1 Mar 2021 |

## Keywords

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

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Dive into the research topics of 'Finite-dimensional irreducible modules of the universal Askey–Wilson algebra at roots of unity'. Together they form a unique fingerprint.## Projects

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