Coupling coefficients of su q (1,1) and multivariate q -Racah polynomials

• Main Authors: Vinet, Luc (Author), Iliev, Plamen (Author), Genest, Vincent (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Elsevier, 2018-07-02T14:29:32Z.
• Subjects: Article
• Online Access: Get fulltext

Gasper & Rahman's multivariate q -Racah polynomials are shown to arise as connection coefficients between families of multivariate q -Hahn or q -Jacobi polynomials. The families of q -Hahn polynomials are constructed as nested Clebsch-Gordan coefficients for the positive-discrete series representations of the quantum algebra suq(1,1) . This gives an interpretation of the multivariate q -Racah polynomials in terms of 3nj symbols. It is shown that the families of q -Hahn polynomials also arise in wavefunctions of q -deformed quantum Calogero-Gaudin superintegrable systems.
Simons Foundation (Grant #280940)
Natural Sciences and Engineering Research Council of Canada