Real fundamental Chevalley involutions and conjugacy classes

Han, Gang; Sun, Binyong

doi:10.1090/proc/16722

Real fundamental Chevalley involutions and conjugacy classes
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by Gang Han and Binyong Sun

Proc. Amer. Math. Soc. 152 (2024), 1493-1499

DOI: https://doi.org/10.1090/proc/16722

Published electronically: February 2, 2024

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Abstract:

Let $\mathsf G$ be a connected reductive linear algebraic group defined over $\mathbb R$, and let $C: \mathsf G\rightarrow \mathsf G$ be a fundamental Chevalley involution. We show that for every $g\in \mathsf G(\mathbb R)$, $C(g)$ 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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