Unipotent character sheaves and strata of a reductive group

TL;DR

This paper establishes a connection between unipotent character sheaves and the stratification of a reductive group, introducing a new parametrization using data from bad characteristic and utilizing the generalized Springer correspondence.

Contribution

It provides a surjective map from unipotent character sheaves to strata and introduces a novel parametrization based on bad characteristic data.

Findings

Defined a surjective map from CS(H) to strata

Provided a new parametrization of CS(H)

Utilized the generalized Springer correspondence

Abstract

Let H be a connected reductive group over an algebraically closed field. We define a surjective map from the set CS(H) of unipotent character sheaves on H (up to isomorphism) to the set of strata of H. To do this we use the generalized Springer correspondence. We also give a new parametrization of CS(H) in terms of data coming from bad characteristic. Some minor errors corrected.