Springer's work on unipotent classes and Weyl group representations

TL;DR

This paper reviews Springer's research on unipotent elements in reductive groups and their connection to Weyl group representations, highlighting key bijections, nonrationality examples, and Springer representations.

Contribution

It summarizes Springer's foundational work on the relationships between unipotent classes and Weyl group representations, including new insights into their properties and examples.

Findings

Springer's bijection between unipotent and nilpotent varieties

Examples of nonrationality in Hecke algebra representations

Springer representations associated with unipotent elements

Abstract

In this paper we discuss some of Springer's work on unipotent elements in a reductive groups and on representations of Weyl groups. Among the topics considered are Springer's bijection from the unipotent variety to the nilpotent variety, Springer's example of nonrationality of certain representations of the Hecke algebras associated to a Weyl group and the Springer representation of the Weyl group associated to a unipotent element.