# Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups

Abstract : We calculate Frobenius-Schur indicator values for some fusion categories obtained from inclusions of finite groups $H\subset G$, where more concretely $G$ is symmetric or alternating, and $H$ is a symmetric, alternating or cyclic group. Our work is strongly related to earlier results by Kashina-Mason-Montgomery, Jedwab-Montgomery, and Timmer for bismash product Hopf algebras obtained from exact factorizations of groups. We can generalize some of their results, settle some open questions and offer shorter proofs; this already pertains to the Hopf algebra case, while our results also cover fusion categories not associated to Hopf algebras.
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https://hal.archives-ouvertes.fr/hal-01122467
Contributor : Peter Schauenburg <>
Submitted on : Wednesday, March 4, 2015 - 7:02:07 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

### Citation

Peter Schauenburg. Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups. Algebras and Representation Theory, Springer Verlag, 2016, 19 (3), pp.645-656. ⟨10.1007/s10468-016-9593-8⟩. ⟨hal-01122467⟩

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