On higher Frobenius-Schur indicators

Authors

  • Y. Liu Jiangxi Normal University
  • W. Willems

Keywords:

irreducible character, higher Frobenius-Schur indicator, Brauer character, permutation module

Abstract

http://dx.doi.org/10.1017/S0004972712000330Similarly to the Frobenius-Schur indicators of irreducible characters we consider higher Frobenius-Schur indicators $\nu_{p^n}(\chi) = \frac{1}{|G|} \sum_{g \in G} \chi(g^{p^n})$ for primes $p$ and $n \in \N$, where $G$ is a finite group and $\chi$ is a generalized character of $G$. It turns out that these invariants give answers to interesting questions in representation theory. In particular, we give several characterizations of groups via higher Frobenius-Schur indicators.

Published

2022-03-08

Issue

Vol. 105 No. 2 (2022)

Section

Articles
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