An Askey–Wilson Algebra of Rank 2

Groenevelt, W.G.M.; Wagenaar, C.C.M.L.

doi:10.3842/SIGMA.2023.008

An Askey–Wilson Algebra of Rank 2

Title

An Askey–Wilson Algebra of Rank 2

Author

Groenevelt, W.G.M. (TU Delft Analysis)
Wagenaar, C.C.M.L. (TU Delft Analysis)

Date

2023

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 U_q (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.

Subject

Askey-Wilson algebra
q-Racah polynomials

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http://resolver.tudelft.nl/uuid:49f90ad1-aa0e-4a4f-8f8d-eecf1e4a98d7

DOI

https://doi.org/10.3842/SIGMA.2023.008

ISSN

1815-0659

Source

Symmetry, Integrability and Geometry: Methods and Applications, 19

Part of collection

Institutional Repository