Tensor product representations of the quantum double of a compact group

Abstract

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the action of the R-matrix, and their decomposition into irreducible *-representations. The example of D(SU(2)) is treated in detail, with explicit formulas for direct integral decomposition (`Clebsch-Gordan series') and Clebsch-Gordan coefficients. We point out possible physical applications.