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Equivariant Tautological Integrals on Flag Varieties
The author apples the Atiyah-Bott-Berline-Vergne formula to the equivariant tautological integrals over flag varieties of types A, B, C, D, and...
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A rim-hook rule for quiver flag varieties
The Abelian/non-Abelian correspondence for cohomology (Martin in Symplectic quotients by a nonabelian group and by its maximal torus.
ar**v:math/0001002... 
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Product structure and regularity theorem for totally nonnegative flag varieties
The totally nonnegative flag variety was introduced by Lusztig. It has enriched combinatorial, geometric, and Lie-theoretic structures. In this...
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Structure constants in equivariant oriented cohomology of flag varieties
We introduce generalized Demazure operators for the equivariant oriented cohomology of the flag variety, which have specializations to various...
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Degenerating products of flag varieties and applications to the Breuil–Mézard conjecture
We consider closed subschemes in the affine grassmannian obtained by degenerating e -fold products of flag varieties, embedded via a tuple of dominant...
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A Gallery Model for Affine Flag Varieties via Chimney Retractions
This paper provides a unified combinatorial framework to study orbits in certain affine flag varieties via the associated Bruhat–Tits buildings. We...
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SYMPLECTIC PBW DEGENERATE FLAG VARIETIES; PBW TABLEAUX AND DEFINING EQUATIONS
We define a set of PBW-semistandard tableaux that is in a weight-preserving bijection with the set of monomials corresponding to integral points in...
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Which Schubert Varieties are Hessenberg Varieties?
After proving that every Schubert variety in the full flag variety of a complex reductive group G is a general Hessenberg variety, we show that not...
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The isomorphism problem for cominuscule Schubert varieties
Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of...
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Grassmannians, Flag Varieties, Schur Functors and Cohomology
In this chapter we introduce the basic theory of flag varieties, and describe general results regarding cohomology groups of line bundles, with an...
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Relative Bott–Samelson Varieties
We prove that, defined with respect to versal flags, the product of two relative Bott–Samelson varieties over a flag bundle is a resolution of...
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Degenerate Affine Flag Varieties and Quiver Grassmannians
We study finite dimensional approximations to degenerate versions of affine flag varieties using quiver Grassmannians for cyclic quivers. We prove...
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Applications of homogeneous fiber bundles to the Schubert varieties
This article explores the relationship between Schubert varieties and equivariant embeddings, using the framework of homogeneous fiber bundles over...
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Cones from quantum groups to tropical flag varieties
We relate quantum degree cones, parametrizing PBW degenerations of quantized envelo** algebras, to (negative tight monomial) cones introduced by...
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Ampleness of Normal Bundles of Base Cycles in Flag Domains
Flag domains are open orbits of noncompact real forms of complex semisimple Lie groups acting on flag manifolds. To each flag domain one can...
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Standard Monomial Theory and Toric Degenerations of Richardson Varieties in Flag Varieties
We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a...