The Real Chevalley Involution
Representation Theory
2019-02-20 v4
Abstract
We consider the Chevalley involution in the context of real reductive groups. We show that if G(R) is the real points of a connected reductive group, there is an involution, unique up to conjugacy by G(R), taking any semisimple element to a conjugate of its inverse. As applications we give a condition for every irreducible representation of G(R) to be self-dual, and to the Frobenius Schur indicator for such groups.
Cite
@article{arxiv.1203.1901,
title = {The Real Chevalley Involution},
author = {Jeffrey Adams},
journal= {arXiv preprint arXiv:1203.1901},
year = {2019}
}