Invariant systems and character sheaves for graded Lie algebras

TL;DR

This paper introduces invariant systems of differential equations to study character sheaves on graded Lie algebras, successfully classifying all cuspidal character sheaves for Vinberg's type I classical graded Lie algebras.

Contribution

It presents a new approach using invariant differential systems to classify cuspidal character sheaves on certain graded Lie algebras.

Findings

Constructed all cuspidal character sheaves for Vinberg's type I classical graded Lie algebras.

Introduced invariant systems of differential equations as a new tool in the study.

Unified previous constructions with new classification results.

Abstract

In this paper we introduce a new ingredient, invariant systems of differential equations, to our study of character sheaves on graded Lie algebras. The character sheaves we construct in this paper, together with the ones constructed in [VX1, X2], constitute all cuspidal character sheaves for Vinberg's type I classical graded Lie algebras.