Geodesic
Drinfeld Doubles for Finite Subgroups of $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ Lie Groups
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

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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], 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: Lie group; fusion categories; conformal field theories; quantum symmetry; Drinfeld doubles. 
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     title = {Drinfeld {Doubles} for {Finite} {Subgroups} of $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ {Lie} {Groups}},
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}
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Robert Coquereaux; Jean-Bernard Zuber. Drinfeld Doubles for Finite Subgroups of $\mathrm{SU}(2)$ and $\mathrm{SU}(3)$ Lie Groups. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a38/

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