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

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.
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Peter Schauenburg. Computing higher Frobenius–Schur indicators in fusion categories constructed from inclusions of finite groups. Pacific Journal of Mathematics, Mathematical Sciences Publishers, 2016, 280 (1), pp.177-201. ⟨10.2140/pjm.2016.280.177⟩. ⟨hal-01115331⟩

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