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arXiv · 1407.6849

Representation and character theory of finite categorical groups

Nora Ganter·Robert Usher
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Abstract

We study the gerbal representations of a finite group $G$ or, equivalently, module categories over Ostrik's category $Vec_G^α$ for a 3-cocycle $α$. We adapt Bartlett's string diagram formalism to this situation to prove that the categorical character of a gerbal representation is a module over the twisted Drinfeld double $D^α(G)$. We interpret this twisted Drinfeld double in terms of the inertia groupoid of a categorical group.

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Nora Ganter, Robert Usher. 2017-01-23. Representation and character theory of finite categorical groups. https://arxiv.org/abs/1407.6849

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