Related papers: The isomorphism problem for Schubert varieties

We prove that the Schubert structure constants of the quantum $K$-theory ring of any minuscule flag variety or quadric hypersurface have signs that alternate with codimension. We also prove that the powers of the deformation parameter $q$…

We consider tangent cones to Schubert subvarieties of the flag variety $G/B$, where $B$ is a Borel subgroup of a reductive complex algebraic group $G$ of type $E_6$, $E_7$ or $E_8$. We prove that if $w_1$ and $w_2$ form a good pair of…

Let $P$ be a parabolic subgroup in $G=SL_n(\mathbf k)$, for $\mathbf k$ an algebraically closed field. We show that there is a $G$-stable closed subvariety of an affine Schubert variety in an affine partial flag variety which is a natural…

For a semisimple adjoint algebraic group $G$ and a Borel subgroup $B$, consider the double classes $BwB$ in $G$ and their closures in the canonical compactification of $G$: we call these closures large Schubert varieties. We show that these…

We study classes determined by the Kazhdan-Lusztig basis of the Hecke algebra in the $K$-theory and hyperbolic cohomology theory of flag varieties. We first show that, in $K$-theory, the two different choices of Kazhdan-Lusztig bases…

Consider a flag variety $Fl$ over an algebraically closed field, and a subvariety $V$ whose cycle class is a multiplicity-free sum of Schubert cycles. We show that $V$ is arithmetically normal and Cohen-Macaulay, in the projective embedding…

We exhibit basic algebro-geometric results on the formal model of semi-infinite flag varieties and its Schubert varieties over an algebraically closed field $\mathbb K$ of characteristic $\neq 2$ from scratch. We show that the formal model…

A Kazhdan-Lusztig variety is the intersection of a locally-closed Schubert cell with an opposite Schubert variety in a flag variety. We present a linear parametrization of the Schubert cells in the affine type A flag variety via…

It is well-known that the $T$-fixed points of a Schubert variety in the flag variety $GL_n(\mathbb{C})/B$ can be characterized purely combinatorially in terms of Bruhat order on the symmetric group $\mathfrak{S}_n$. In a recent preprint,…

This article explores the relationship between Schubert varieties and equivariant embeddings, using the framework of homogeneous fiber bundles over flag varieties. We show that the homogenous fiber bundles obtained from…

We introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag…

We show that various genus zero Gromov-Witten invariants for flag varieties representing different homology classes are indeed the same. In particular, many of them are classical intersection numbers of Schubert cycles.

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary…

We prove a conjecture of A. S. Buch concerning the structure constants of the Grothendieck ring of a flag variety with respect to its basis of Schubert structure sheaves. For this, we show that the coefficients in this basis of the…

We show that given two smooth affine varieties over $\mathbb{C}$ such that their rings of differential operators are Morita equivalent, then corresponding cotangent bundles are isomorphic as symplectic varieties.

We consider the action of the Levi subgroup of a parabolic subgroup that stabilizes a Schubert variety. We show that a smooth Schubert variety is a homogeneous space for a parabolic subgroup, or it has a smooth Schubert divisor. Further, we…

We state a precise conjectural isomorphism between localizations of the equivariant quantum K-theory ring of a flag variety and the equivariant K-homology ring of the affine Grassmannian, in particular relating their Schubert bases and…

Under the assumption that the base field k has characteristic 0, we compute the algebraic cobordism fundamental classes of a family of Schubert varieties isomorphic to full and symplectic flag bundles. We use this computation to prove a…

We provide a method for gluing (small) resolutions of singularities of Schubert varieties \(X_w\). An explicit isomorphism of \(X_w\) with an (iterated) bundle is constructed when \(w\) has an (iterated) BP decomposition. Combined with the…

Regular semisimple Hessenberg varieties are a family of subvarieties of the flag variety that arise in number theory, numerical analysis, representation theory, algebraic geometry, and combinatorics. We give a "Giambelli formula" expressing…