Coupling coefficients for tensor product representations of quantum SU(2)
- Delft Institute of Applied Mathematics (DIAM), Technische Universiteit Delft, PO Box 5031, 2600 GA Delft (Netherlands)
We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. 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.
- OSTI ID:
- 22305853
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 55; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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