Representation and character theory of finite categorical groups

Abstract

We study the gerbal representations of a finite group G or, equivalently, module categories over Ostrik’s category VecαG 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 representation of the inertia groupoid of a categorical group. We interpret such a representation as a module over the twisted Drinfeld double Dα(G).