An Askey–Wilson Algebra of Rank 2
Wolter Groenevelt (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Carel Wagenaar (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
An algebra is introduced which can be considered as a rank 2 extension of the Askey–Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum algebra Uq (sl(2, C)). It is shown that bivariate q-Racah polynomials appear as overlap coefficients of eigenvectors of generators of the algebra. Furthermore, the corresponding q-difference operators are calculated using the defining relations of the algebra, showing that it encodes the bispectral properties of the bivariate q-Racah polynomials.
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