Computing higher Frobenius–Schur indicators in fusion categories constructed from inclusions of finite groups

Peter Schauenburg

Vol. 280 (2016), No. 1, 177–201

DOI: 10.2140/pjm.2016.280.177

Abstract

We consider a subclass of the class of group-theoretical fusion categories: To every finite group $G$ and subgroup $H$ one can associate the category of $G$-graded vector spaces with a two-sided $H$-action compatible with the grading. We derive a formula that computes higher Frobenius-Schur indicators for the objects in such a category using the combinatorics and representation theory of the groups involved in their construction. We calculate some explicit examples for inclusions of symmetric groups.

Keywords

fusion category, Frobenius-Schur indicator

Mathematical Subject Classification 2010

Primary: 18D10, 16T05

Secondary: 20C15

Milestones

Received: 13 August 2014

Revised: 23 January 2015

Accepted: 26 February 2015

Published: 28 December 2015