A Higher Frobenius–Schur Indicator Formula for Group-Theoretical Fusion Categories

Abstract : Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: A finite group G endowed with a three-cocycle ω, and a subgroup H ⊂ G endowed with a two-cochain whose coboundary is the restriction of ω. The objects of the category are G-graded vector spaces with suitably twisted H-actions; the associativity of tensor products is controlled by ω. Simple objects are parametrized in terms of projective representations of finite groups, namely of the stabilizers in H of right H-cosets in G, with respect to two-cocycles defined by the initial data. We derive and study general formulas that express the higher Frobenius-Schur indicators of simple objects in a group-theoretical fusion category in terms of the group-theoretical and cohomological data defining the category and describing its simples.
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Peter Schauenburg. A Higher Frobenius–Schur Indicator Formula for Group-Theoretical Fusion Categories. Communications in Mathematical Physics, Springer Verlag, 2015, 340 (2), pp.833-849. ⟨http://link.springer.com/article/10.1007/s00220-015-2437-2⟩. ⟨10.1007/s00220-015-2437-2⟩. ⟨hal-01115411⟩

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