A computational approach to the Frobenius–Schur indicators of finite exceptional groups

Abstract

We prove that the finite exceptional groups [Formula: see text], [Formula: see text], and [Formula: see text] have no irreducible complex characters with Frobenius–Schur indicator [Formula: see text], and we list exactly which irreducible characters of these groups are not real-valued. We also give a complete list of complex irreducible characters of the Ree groups [Formula: see text] which are not real-valued, and we show the only character of this group which has Frobenius–Schur indicator [Formula: see text] is the cuspidal unipotent character [Formula: see text] found by Geck.