Mackey formula in type A

Abstract

Let G be a connected reductive group defined over a finite field with q elements and let F: G → G be the corresponding Frobenius endomorphism. We prove that the Mackey formula for Lusztig induction and restriction holds in GF if all the simple components of G are of type A. Our result holds for every Frobenius endomorphism (split or non-split) and for every q. 1991 Mathematics Subject Classification: 20G05, 20G40.