# Representation and character theory of finite categorical groups

## Nora Ganter and Robert Usher

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

Keywords: categorical groups, representation theory, inertia groupoid, drinfeld double

2010 MSC: 20J99, 20N99

Theory and Applications of Categories, Vol. 31, 2016, No. 21, pp 542-570.

Published 2016-06-22.

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