1 results
ON HIGHER FROBENIUS–SCHUR INDICATORS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 105 / Issue 2 / April 2022
- Published online by Cambridge University Press:
- 12 July 2021, pp. 267-277
- Print publication:
- April 2022
-
- Article
- Export citation
-
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.
