Nikolaus Conference 2023

Speaker: Sergio Cia (Paris)

Title: A Mackey Formula for Non-Connected Reductive Groups

Abstract:

The Mackey formula is an important tool on representation theory of finite groups. The existence of an adaptation for the Deligne-Lusztig functors is quite helpful for their study. For a finite group \(\mathbf G^F\) coming from a non-connected algebraic group \(\mathbf G\), we had formulas given by Fran├žois Digne and Jean Michel that only worked in some connected components of \(\mathbf G\). In this exposition, we will present a modification of the Mackey Formula for Levis of finite reductive groups that will work on the whole group. And we will give some conditions on \(\mathbf G\) under which the formula will hold.

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