Tensor Product Representations of the Quantum Double of a Compact Group

Abstract:

We consider the quantum double of a compact group G, following an earlier paper. We use the explicit comultiplication on 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 is treated in detail, with explicit formulas for direct integral decomposition (“Clebsch–Gordan series”) and Clebsch-Gordan coefficients. We point out possible physical applications.