Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(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.