Tensor Product Representations of the Quantum Double of a Compact Group
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/ Abstract
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.
Journal: Communications in Mathematical Physics