Families and Springer's correspondence

TL;DR

This paper links the parametrization of irreducible Weyl group representations with Springer's correspondence and describes unipotent character sheaves via conjugacy class restrictions.

Contribution

It introduces a new relation between Weyl group representations and Springer's correspondence, and provides a parametrization of unipotent character sheaves.

Findings

Established a relation between Weyl group representations and Springer's correspondence.

Outlined a parametrization of unipotent character sheaves.

Connected representation theory with geometric objects in reductive groups.

Abstract

We establish a relation between the known parametrization of a family of irreducible representations of a Weyl group and Springer's correspondence. We outline a parametrization of unipotent character sheaves on a connected reductive group in terms of restrictions to various conjugacy classes.