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ON HIGHER FROBENIUS–SCHUR INDICATORS

Published online by Cambridge University Press:  12 July 2021

YANJUN LIU*
Affiliation:
School of Mathematics and Statistics, Jiangxi Normal University, Nanchang330022, China
WOLFGANG WILLEMS
Affiliation:
Universität Magdeburg, Magdeburg, Germany and Universidad del Norte, Barranquilla, Colombia e-mail: [email protected]

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.

Type
Research Article
Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Both authors were supported by NSFC (11661042 and 11761034) and the Natural Science Foundation of Jiangxi Province (20192ACB21008).

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