Z/m-graded Lie algebras and perverse sheaves, I

TL;DR

This paper introduces a block decomposition of the equivariant derived category for cyclically graded Lie algebras, extending the generalized Springer correspondence to a graded context.

Contribution

It generalizes the Springer correspondence by developing a block decomposition framework for graded Lie algebras and their associated derived categories.

Findings

Established a block decomposition for the equivariant derived category.

Extended Springer correspondence to cyclically graded Lie algebras.

Provided new tools for studying graded Lie algebra representations.

Abstract

We give a block decomposition of the equivariant derived category arising from a cyclically graded Lie algebra. This generalizes certain aspects of the generalized Springer correspondence to the graded setting.