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Frobenius-Schur Indicators for Some Fusion Categories Associated to Symmetric and Alternating Groups

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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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  1. Institut de Mathématiques de Bourgogne, UMR5584 CNRS, Université Bourgogne Franche-Comté, 21000, Dijon, France

    Peter Schauenburg

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  1. Peter Schauenburg
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Correspondence to Peter Schauenburg.

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Presented by Susan Montgomery.

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Schauenburg, P. Frobenius-Schur Indicators for Some Fusion Categories Associated to Symmetric and Alternating Groups. Algebr Represent Theor 19, 645–656 (2016). https://doi.org/10.1007/s10468-016-9593-8

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  • DOI: https://doi.org/10.1007/s10468-016-9593-8

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