Toward a Mackey formula for compact restriction of character sheaves

TL;DR

This paper extends a Mackey-type formula to the compact restriction of semisimple perverse sheaves derived from character sheaves, aiding in the correspondence between character sheaves and admissible representations.

Contribution

It generalizes a previous result to a new Mackey formula for compact restriction, enhancing tools for matching character sheaves with admissible representations.

Findings

Established a Mackey formula for compact restriction of character sheaves

Provided conditions under which the formula applies

Facilitated better matching of character sheaves with representations

Abstract

We generalize a result by Cunningham-Salmasian to a Mackey-type formula for the compact restriction of a semisimple perverse sheaf produced by parabolic induction from a character sheaf, under certain conditions on the parahoric group used to define compact restriction. This provides new tools for matching character sheaves with admissible representations.