Robert Usher | Searcharxiv

arXiv2017

Representation and character theory of finite categorical groups

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.

math.CT↗

arXiv2016

Fermionic 6$j$-symbols in superfusion categories

We describe how the study of superfusion categories (roughly speaking, fusion categories enriched over the category of super vector spaces) reduces to that of fusion categories over sVect, in the sense of Drinfeld, Gelaki, Nikshych, and Ostrik. Following Brundan and Ellis, we give the construction of the underlying fusion category of a superfusion category, and give an explicit formula for the associator in this category in terms of 6$j$-symbols. We give a definition of the $π$-Grothendieck ring of a superfusion category, and prove a version of Ocneanu rigidity for superfusion categories.

math.QA↗