ON HIGHER FROBENIUS-SCHUR INDICATORS

Similarly to the Frobenius-Schur indicator of irreducible characters, we consider higher Frobenius-Schur indicators nu(pn)(chi) = vertical bar G vertical bar(-1) Sigma(g is an element of G)chi(g(pn)) for primes p and n is an element of 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.