Equivariant Sheaves on Flag Varieties

TL;DR

This paper proves a conjecture relating Borel-equivariant sheaves on flag varieties to dg modules, establishing an equivalence of categories that advances understanding in geometric representation theory.

Contribution

It establishes an equivalence between the Borel-equivariant derived category of sheaves on flag varieties and the perfect derived category of dg modules, confirming a conjecture by Soergel and Lunts.

Findings

Proves the conjecture for flag varieties.

Establishes an equivalence of categories in geometric representation theory.

Advances understanding of sheaf categories on flag varieties.

Abstract

We show that the Borel-equivariant derived category of sheaves on the flag variety of a complex reductive group is equivalent to the perfect derived category of dg modules over the extension algebra of the direct sum of the simple equivariant perverse sheaves. This proves a conjecture of Soergel and Lunts in the case of flag varieties.