Higher Frobenius-Schur indicators for Drinfeld doubles of finite groups through characters of centralizers

Abstract : We present a new approach to calculating the higher Frobenius-Schur indicators for the simple modules over the Drinfeld double of a finite group. In contrast to the formula by Kashina-Sommerhäuser-Zhu that involves a sum over all group elements satisfying a certain condition, our formula operates on the level of conjugacy classes and character tables. It can be implemented in the computer algebra system GAP, efficiently enough to deal, on a laptop, with symmetric groups up to S_18 (providing further evidence that indicators are non-negative in this case) or simple groups of order up to 2 · 10^8. The approach also allows us to test whether all indicators over the double of a given group are rational , without computing them. Among simple groups of order up to about 5 · 10^11 an inspection yields exactly one example (of order about 5 · 10^9) where irrational indicators occur.
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https://hal.archives-ouvertes.fr/hal-01293978
Contributeur : Peter Schauenburg <>
Soumis le : mercredi 30 mars 2016 - 10:40:57
Dernière modification le : mardi 12 avril 2016 - 11:15:55
Document(s) archivé(s) le : lundi 14 novembre 2016 - 06:41:10

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  • HAL Id : hal-01293978, version 1
  • ARXIV : 1604.02378

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Peter Schauenburg. Higher Frobenius-Schur indicators for Drinfeld doubles of finite groups through characters of centralizers. 2016. <hal-01293978>

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