Coupling coefficients for tensor product representations of quantum $\mathrm{SU}(2)$

Abstract

We study tensor products of infinite dimensional representations (not corepresentations) of the $\mathrm{SU}(2)$ quantum group. Eigenvectors of certain self-adjoint elements are obtained, and coupling coefficients between different eigenvectors are computed. The coupling coefficients can be considered as $q$-analogs of Bessel functions. As a results we obtain several $q$-integral identities involving $q$-hypergeometric orthogonal polynomials and $q$-Bessel-type functions.

31 pages. Parts of the paper are from my unpublished notes "Tensor products for quantum SU(2)" from 2004

References in corpus (2)

• Orthogonality relations for Al-Salam--Carlitz polynomials of type II
• The indeterminate moment problem for the $q$-Meixner polynomials

Cited by in corpus (3)

• Orthogonality relations for Al-Salam--Carlitz polynomials of type II
• $S{U}_q(3)$ corepresentations and bivariate $q$-Krawtchouk polynomials
• $3nj$-symbols and identities for $q$-Bessel functions