Related papers: Structure constants for Chern classes of Schubert …
We present a finite-dimensional and smooth formulation of string structures on spin bundles. It uses trivializations of the Chern-Simons 2-gerbe associated to this bundle. Our formulation is particularly suitable to deal with string…
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…
Nakada's colored hook formula is a vast generalization of many important formulae in combinatorics, such as the classical hook length formula and the Peterson's formula for the number of reduced expressions of minuscule Weyl group elements.…
Structure constants for the multiplication of Schubert polynomials by Schur symmetric polynomials are known to be related to the enumeration of chains in a new partial order on S_\infty, which we call the universal k-Bruhat order. Here we…
We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the…
Let X be the flag variety of the symplectic group. We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of X. We use these polynomials to…
We propose a new approach to the multiplication of Schubert classes in the K-theory of the flag variety. This extends the work of Fomin and Kirillov in the cohomology case, and is based on the quadratic algebra defined by them. More…
Pak-Robichaux recently introduced a signed puzzle rule for Schubert structure constants, which they use to show that sums $\gamma_k(n)$ of these constants with a bounded number of inversions are polynomial. We give a different, conceptual…
In this paper, a description of the set-theoretical defining equations of symplectic (type C) Grassmannian/flag/Schubert varieties in corresponding (type A) algebraic varieties is given as linear polynomials in Pl$\ddot{u}$cker coordinates,…
We construct a basis of the equivariant $K$-theory of Bott towers, and we describe precisely the multiplicative structure of these algebras. We deduce similar results for Bott-Samelson varieties. Thanks to the link between flag varieties…
We study the ring theory of the multiparameter deformations of the quantum Schubert cell algebras obtained from 2-cocycle twists. This is a large family, which extends the Artin-Schelter-Tate algebras of twisted quantum matrices. We…
We introduce a mutation algorithm for puzzles that is a three-direction analogue of the classical jeu de taquin algorithm for semistandard tableaux. We apply this algorithm to prove our conjectured puzzle formula for the equivariant…
Using combinatorial properties of symmetric polynomials, we compute explicitly the Soergel modules for some permutations whose corresponding Schubert varieties are rationally smooth. We build from them diagram algebras whose module…
We study the Castelnuovo-Mumford regularity of tangent cones of Schubert varieties. Conjectures about this statistic are presented; these are proved for the covexillary case. This builds on work of L. Li and the author on these tangent…
In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way…
The ring K(G/B) is isomorphic to a quotient of a Laurent polynomial ring by an ideal generated by certain W-symmetric functions and has a basis given by classes O_w, where O_w is the class of the structure sheaf of the Schubert variety X_w.…
One describes, using a detailed analysis of Atiyah--Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This…
We introduce the notion of a cominuscule point in a Schubert variety in a generalized flag variety for a semisimple group. We derive formulas expressing the Hilbert series and multiplicity of a Schubert variety at a cominuscule point in…
A Schubert class is called rigid if it can only be represented by Schubert varieties. The rigid Schubert classes have been classified in Grassmannians and orthogonal Grassmannians. In this paper, we study the rigidity problem in partial…
In this paper we give a nice formula for the Castelnuovo-Mumford regularity of the Segre product of modules, under some suitable hypotheses. This extends recent results of David A. Cox, and Evgeny Materov (2009).