Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))

Abstract

The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch-Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah-Wigner coefficients. This kernel is explicitly calculated.