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Representation and character theory of finite categorical groups
Theory and applications of categories, Tome 31 (2016), pp. 542-570 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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 $D^\alpha(G)$.

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Classification : 20J99, 20N99
Keywords: categorical groups, representation theory, inertia groupoid, drinfeld double 
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     author = {Nora Ganter and Robert Usher},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2016_31_a20/}
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Nora Ganter; Robert Usher. Representation and character theory of finite categorical groups. Theory and applications of categories, Tome 31 (2016), pp. 542-570. http://geodesic.mathdoc.fr/item/TAC_2016_31_a20/