Real fundamental Chevalley involutions and conjugacy classes

2021/05/04 by Han, Gang, Sun, Binyong
#20G20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2105.01273

Abstract

Let \mathsf G be a connected reductive linear algebraic group defined over \mathbb R, and let C: \mathsf G→ \mathsf G be a fundamental Chevalley involution. We show that for every g∈ \mathsf G(\mathbb R), C(g) is conjugate to g^-1 in the group \mathsf G(\mathbb R). Similar result on the Lie algebras is also obtained.

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