Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Mackey formula for disconnected reductive groups

Sergio Cía

Abstract

We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.

Mackey formula for disconnected reductive groups

Abstract

We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.
Paper Structure (4 sections, 8 theorems, 35 equations)

This paper contains 4 sections, 8 theorems, 35 equations.

Table of Contents

  1. Introduction.
  2. General setting.
  3. Green functions over $\mathbf G$ and generalised character formula.
  4. General Mackey formula.

Key Result

Theorem 1.1

Let us assume that $\mathbf G/\mathbf G^{\circ}$ consists on semisimple elements and that it has "enough normal subgroups" (see Corollary main_corollary). Let $\mathbf L$ and $\mathbf M$ be Levi subgroups of $\mathbf G$ (in a sense to be precised in § 2). Then the Mackey formula holds under the same

Theorems & Definitions (16)

  • Theorem 1.1
  • Proposition 3.1: Generalized character formula
  • Remark
  • proof
  • Lemma 3.2
  • proof
  • Proposition 3.3: Exchange formulae
  • proof
  • Proposition 4.1
  • proof
  • ...and 6 more