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Representation and character theory of finite categorical groups

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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.

http://www.tac.mta.ca/tac/volumes/31/21/31-21.pdf

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