Modular generalized Springer correspondence: an overview

TL;DR

This paper provides an overview of the modular generalized Springer correspondence, discussing its foundational ideas, recent developments, and the role of modular character sheaves within algebraic group representation theory.

Contribution

It expands on previous work by including new discussions on modular character sheaves and geometric functors, offering insights into the modular Springer correspondence.

Findings

Discussion of modular character sheaves

Heuristic remarks on parabolic induction and restriction

Overview of recent developments in the modular Springer correspondence

Abstract

This is an overview of our series of papers on the modular generalized Springer correspondence. It is an expansion of a lecture given by the second author in the Fifth Conference of the Tsinghua Sanya International Mathematics Forum, Sanya, December 2014, as part of the Master Lecture `Algebraic Groups and their Representations' Workshop honouring G. Lusztig. The material that has not appeared in print before includes some discussion of the motivating idea of modular character sheaves, and heuristic remarks about geometric functors of parabolic induction and restriction.