Computational proof of the Mackey formula for q > 2

TL;DR

This paper proves that the Mackey formula for Lusztig induction and restriction holds in connected reductive groups over finite fields for q>2 or when the group lacks an E-type component.

Contribution

It provides a proof confirming the Mackey formula's validity under specific conditions, extending previous results in representation theory of finite groups of Lie type.

Findings

Mackey formula holds for q>2 in connected reductive groups.

The formula also holds when the group has no E-type component.

Results apply to Lusztig induction and restriction in finite groups.

Abstract

Let G be a connected reductive group defined over a finite field with q elements. We prove that the Mackey formula for the Lusztig induction and restriction holds in G whenever q>2 or G does not have a component of type E.