相关论文: Recognizing Schubert cells

Computations in small Coxeter groups or dihedral groups suggest that the partition into Kazhdan-Lusztig cells with unequal parameters should obey to some semicontinuity phenomenon (as the parameters vary). The aim of this paper is to…

We study generalizations of Schur functors from categories consisting of flags of vector spaces. We give different descriptions of the category of such functors in terms of representations of certain combinatorial categories and infinite…

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical…

We first describe the tangent space to the affine flag manifold associated to a simple algebraic group over $\mathbb{C}$ at the distinguished point starting from standard definitions. We then construct projective lines in the affine flag…

We give a detailed analysis of the orbit structure of the third power of the flag variety attached to SL(3,R). It turns out that 36 generalized Schubert cells split into 70 orbits plus one continuous family of orbits. On the latter, we…

The totally nonnegative part of a partial flag variety G/P is known to have a decomposition into semi-algebraic cells. We show that the closure of a cell is again a union of cells and give a combinatorial description of the closure…

These are extended notes of a talk given at Maurice Auslander Distinguished Lectures and International Conference (Woods Hole, MA) in April 2013. Their aim is to give an introduction into Schubert calculus on Grassmannians and flag…

We give a permutation pattern avoidance criteria for determining when the projection map from the flag variety to a Grassmannian induces a fiber bundle structure on a Schubert variety. In particular, we introduce the notion of a split…

Schur functions satisfy the relative Pl\"ucker relations which describe the projective embedding of the flag varieties and the Hirota bilinear equations for the modified KP hierarchies. These relative Pl\"ucker relations are generalized to…

We systematically study the splitting of vector bundles on a smooth, projective variety, whose restriction to the zero locus of a regular section of an ample vector bundle splits. First, we find ampleness and genericity conditions which…

Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For `hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that…

Cerulli Irelli and Lanini have shown that PBW degenerations of flag varieties in type A and C are actually Schubert varieties of higher rank. We introduce Dynkin cones to parameterise specific abelianisations of classical Lie algebras.…

We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras…

Schubert varieties in the full flag variety of Kac-Moody type are indexed by elements of the corresponding Weyl group. We give a practical criterion for when two such Schubert varieties (from potentially different flag varieties) are…

Schubert varieties have been exhaustively studied with a plethora of techniques: Coxeter groups, explicit desingularization, Frobenius splitting, etc. Many authors have applied these techniques to various other varieties, usually defined by…

We give examples of non-perverse parity sheaves on Schubert varieties for all primes.

We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety of Lie type A via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect…

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…

For each $A\in\N^n$ we define a Schubert variety $\sh_A$ as a closure of the $\Slt(\C[t])$-orbit in the projectivization of the fusion product $M^A$. We clarify the connection of the geometry of the Schubert varieties with an algebraic…

We provide a proof that every Schubert variety of a semi-infinite flag variety is projectively normal. This gives us an interpretation of a Demazure module of a global Weyl module of a current Lie algebra as the (dual) space of the space of…