The Real Chevalley Involution

Details The Real Chevalley Involution The Real Chevalley Involution

2012-03-08

arxiv.org/abs/1203.1901v1

Mathematics

Representation Theory

Scientific paper

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.

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