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arXiv · 1405.5782

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

Wolter Groenevelt
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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.

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Wolter Groenevelt. 2014-05-22. Coupling coefficients for tensor product representations of quantum $\mathrm{SU}(2)$. https://doi.org/10.1063/1.4898561

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