Vol. 280, No. 1, 2016

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

Peter Schauenburg

Vol. 280 (2016), No. 1, 177–201

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.

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fusion category, Frobenius-Schur indicator
Mathematical Subject Classification 2010
Primary: 18D10, 16T05
Secondary: 20C15
Received: 13 August 2014
Revised: 23 January 2015
Accepted: 26 February 2015
Published: 28 December 2015
Peter Schauenburg
Institut de Mathématiques de Bourgogne
Université Bourgogne Franche-Comté
F-21000 Dijon