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Quantum Analogs of Tensor Product Representations of $\mathfrak{su}(1,1)$
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study representations of $\mathcal U_q(\mathfrak{su}(1,1))$ that can be considered as quantum analogs of tensor products of irreducible $*$-representations of the Lie algebra $\mathfrak{su}(1,1)$. We determine the decomposition of these representations into irreducible $*$-representations of $\mathcal U_q(\mathfrak{su}(1,1))$ 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.
Keywords: tensor product representations; Clebsch–Gordan coefficients; big $q$-Jacobi functions. 
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     author = {Wolter Groenevelt},
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Wolter Groenevelt. Quantum Analogs of Tensor Product Representations of $\mathfrak{su}(1,1)$. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a76/

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