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ON HIGHER FROBENIUS–SCHUR INDICATORS
Published online by Cambridge University Press: 12 July 2021
Abstract
Similarly to the Frobenius–Schur indicator of irreducible characters, we consider higher Frobenius–Schur indicators
$\nu _{p^n}(\chi ) = |G|^{-1} \sum _{g \in G} \chi (g^{p^n})$
for primes p and
$n \in \mathbb {N}$
, where G is a finite group and
$\chi $
is a generalised character of G. These invariants give answers to interesting questions in representation theory. In particular, we give several characterisations of groups via higher Frobenius–Schur indicators.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2021 Australian Mathematical Publishing Association Inc.
Footnotes
Both authors were supported by NSFC (11661042 and 11761034) and the Natural Science Foundation of Jiangxi Province (20192ACB21008).
References
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