Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups
Abstract
Drinfeld doubles of finite subgroups of SU(2) and SU(3) are investigated in detail. Their modular data - S, T and fusion matrices - are computed explicitly, and illustrated by means of fusion graphs. This allows us to reexamine certain identities on these tensor product or fusion multiplicities under conjugation of representations that had been discussed in our recent paper [J. Phys. A: Math. Theor. 44 (2011), 295208, 26 pages, arXiv:1103.2943], proved to hold for simple and affine Lie algebras, and found to be generally wrong for finite groups. It is shown here that these identities fail also in general for Drinfeld doubles, indicating that modularity of the fusion category is not the decisive feature. Along the way, we collect many data on these Drinfeld doubles which are interesting for their own sake and maybe also in a relation with the theory of orbifolds in conformal field theory.
Keywords
Cite
@article{arxiv.1212.4879,
title = {Drinfeld Doubles for Finite Subgroups of SU(2) and SU(3) Lie Groups},
author = {Robert Coquereaux and Jean-Bernard Zuber},
journal= {arXiv preprint arXiv:1212.4879},
year = {2013}
}
Comments
v2: Added references. Corrected typos. Revised argument in section 3.2, results unchanged. Fig. 15 redrawn (one component of the graph was missing). Minor modifications in Abstract and Introduction. Redundant information removed. Text slightly shortened. v3: Published version. v4: misprints are corrected