Galois group action and Jordan decomposition of characters of finite reductive groups with connected center

Abstract

Let G be a connected reductive group with connected center defined over Fq, with Frobenius morphism F. Given an irreducible complex character χ of GF with its Jordan decomposition, and a Galois automorphism σ∈Gal(Q‾/Q), we give the Jordan decomposition of the image χσ of χ under the action of σ on its character values.