文摘
We show that several character correspondences for finite reductive groups $G$ are equivariant with respect to group automorphisms under the additional assumption that the linear algebraic group associated to $G$ has connected center. The correspondences we consider are the so-called Jordan decomposition of characters introduced by Lusztig and the generalized Harish-Chandra theory of unipotent characters due to BrouCMalleichel. In addition we consider a correspondence giving character extensions, due to the second author, in order to verify the inductive McKay condition from Isaacsalleavarro for the non-abelian finite simple groups of Lie types $^3\mathsf{D }_4,\mathsf{E }_8,\mathsf{F }_4,^2\mathsf{F }_4$ , and $\mathsf{G }_2$ .