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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 Falgebra 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 finitedimensional 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 

Pages (fromto)  1229 
Number of pages  18 
Journal  Journal of Algebra 
Volume  569 
DOIs  
State  Published  1 Mar 2021 
Keywords
 Askey–Wilson algebras
 Chebyshev polynomials
 qRacah sequences
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Dive into the research topics of 'Finitedimensional irreducible modules of the universal Askey–Wilson algebra at roots of unity'. Together they form a unique fingerprint.Projects
 1 Finished

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