Staggered sheaves on partial flag varieties

TL;DR

This paper demonstrates that the derived category of equivariant coherent sheaves on partial flag varieties admits an artinian staggered t-structure, leading to a basis for equivariant K-theory from simple staggered sheaves.

Contribution

It establishes the existence of an artinian staggered t-structure on partial flag varieties and constructs a basis for their equivariant K-theory using simple staggered sheaves.

Findings

Existence of an artinian staggered t-structure on partial flag varieties.

Construction of a basis for equivariant K-theory from simple staggered sheaves.

Advancement in understanding the structure of derived categories on flag varieties.

Abstract

Staggered $t$-structures are a class of $t$-structures on derived categories of equivariant coherent sheaves. In this note, we show that the derived category of coherent sheaves on a partial flag variety, equivariant for a Borel subgroup, admits an artinian staggered $t$-structure. As a consequence, we obtain a basis for its equivariant $K$-theory consisting of simple staggered sheaves.