Tensor product representations of the quantum double of a compact group
q-alg
2009-10-30 v3 High Energy Physics - Theory
Quantum Algebra
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.
Cite
@article{arxiv.q-alg/9712042,
title = {Tensor product representations of the quantum double of a compact group},
author = {T. H. Koornwinder and F. A. Bais and N. M. Muller},
journal= {arXiv preprint arXiv:q-alg/9712042},
year = {2009}
}
Comments
LaTeX2e, 27 pages, corrected references, accepted by Comm.Math.Phys