Abstract
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.
Publisher
Cambridge University Press (CUP)