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arXiv · 1104.5101

Quantum Analogs of Tensor Product Representations of su(1,1)

Wolter Groenevelt
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Abstract

We study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible *-representations of $U_q(su(1,1))$ by diagonalizing the action of the Casimir operator on suitable subspaces of the representation spaces. This leads to an interpretation of the big $q$-Jacobi polynomials and big $q$-Jacobi functions as quantum analogs of Clebsch-Gordan coefficients.

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BibTeXRIS

Wolter Groenevelt. 2011-08-09. Quantum Analogs of Tensor Product Representations of su(1,1). https://doi.org/10.3842/sigma.2011.077

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