Partial flag varieties, stable envelopes, and weight functions

G-stable pieces and partial flag varieties

We will use the combinatorics of the G-stable pieces to describe the closure relation of the partition of partial flag varieties in [L3, section 4].

Staggered Sheaves on Partial Flag Varieties

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. Let X be a vari...

Smooth Schubert Varieties in Partial Flag Manifolds

Critical Points of Master Functions and Flag Varieties

We consider critical points of master functions associated with integral dominant weights of Kac-Moody algebras and introduce a generating procedure constructing new critical points starting from a given one. The set of all critical points constructed from a given one is called a population. We formulate a conjecture that a population is isomorphic to the flag variety of the Langlands dual Kac-...

A Partial Horn Recursion in the Cohomology of Flag Varieties

Horn recursion is a term used to describe when non-vanishing products of Schubert classes in the cohomology of complex flag varieties are characterized by inequalities parameterized by similar non-vanishing products in the cohomology of “smaller” flag varieties. We consider the type A partial flag variety and find that its cohomology exhibits a Horn recursion on a certain deformation of the cup...