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

2019/05/22 by Trefethen, Stephen, Vinroot, C. Ryan
#20C33 #20C40 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1905.09379

Abstract

We prove that the finite exceptional groups F₄(q), E₇(q)_ad, and E₈(q) have no irreducible complex characters with Frobenius-Schur indicator -1, and we list exactly which irreducible characters of these groups are not real-valued. We also give an exact list of complex irreducible characters of the Ree groups ² F₄(q²) which are not real-valued, and we show the only character of this group which has Frobenius-Schur indicator -1 is the cuspidal unipotent character χ₂₁ found by M. Geck.

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