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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
- 1 Finished
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The Unversial Racah Algebra and Its Applications(4/4)
Huang, H.-W. (PI)
1/08/20 → 31/07/21
Project: Research