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The decomposition of tensor products of representations into irreducibles isstudied for a continuous family of integrable operator representations of$U_q(sl(2,R)$. It is described by an explicit integral transformation involvinga distributional kernel that can be seen as an analogue of the Clebsch-Gordancoefficients. Moreover, we also study the relation between two canonicaldecompositions of triple tensor products into irreducibles. It can berepresented by an integral transformation with a kernel that generalizes theRacah-Wigner coefficients. This kernel is explicitly calculated.Comment: 39 pages, AMS-Latex; V2: Added comments and references concerning  relation to Faddeev's modular double, minor corrections, version to be  published in CM

Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(2, ℝ))