Related papers: Boolean Schubert Structure Coefficients

We establish a Schubert calculus for Bott-Samelson resolutions in the algebraic cobordism ring of a complete flag variety G/B.

We study the conditions under which a K\"ahlerian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^*M$ of a Riemannian manifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that a certain…

We determine explicitly all structure constants of the whole chiral BRST cohomology ring in $D=2$ string theory including both the discrete states and tachyon states. This is made possible by establishing several identities for Schur…

We define degeneracy loci for vector bundles with structure group $G_2$, and give formulas for their cohomology (or Chow) classes in terms of the Chern classes of the bundles involved. When the base is a point, such formulas are part of the…

The "back-stabilization number" for products of Schubert polynomials is the distance the corresponding permutations must be shifted before the structure constants stabilize. We give an explicit formula for this number and thereby prove a…

This paper investigates stable cohomotopy groups in codimensions two and three from complementary algebraic and geometric viewpoints. For general CW complexes, we give a complete characterization of stable cohomotopy in codimension two and…

Schubert polynomials are a basis for the polynomial ring that represent Schubert classes for the flag manifold. In this paper, we introduce and develop several new combinatorial models for Schubert polynomials that relate them to other…

In a $n$-dimensional Lie algebra, random numerical values are assigned by computer to $n(n-1)$ especially selected structure constants. An algorithm is then created, which calculates without ambiguity the remaining constants, obeying the…

In this letter we make a brief review of some basic properties (the matrix elements, the trace, the Glauber formula) of coherent operators and study the corresponding ones for generalized coherent operators based on Lie algebra su(1,1). We…

We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…

This chapter combines an introduction and research survey about Schubert varieties. The theme is to combinatorially classify their singularities using a family of polynomial ideals generated by determinants.

Define a ``truncation'' $r_{t}(p)$ of a polynomial $p$ in $\{x_1,x_2,x_3,...\}$ as the polynomial with all but the first $t$ variables set to zero. In certain good cases, the truncation of a Schubert or Grothendieck polynomial may again be…

We relate Kostant's theorem on the cohomology of a flag manifold $G/B$ with the geometry of the Bruhat-Poisson structure. We express Kostant's harmonic forms in terms of the moment maps (for the torus action) and the Liouville volume forms…

Chow rings of flag varieties have bases of Schubert cycles $\sigma_u$, indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula for the structure constants of this basis. The celebrated…

This paper studies the Sobolev regularity estimates of weak solutions of a class of singular quasi-linear elliptic problems of the form $u_t - \mbox{div}[\mathbb{A}(x,t,u,\nabla u)]= \mbox{div}[{\mathbf F}]$ with homogeneous Dirichlet…

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 compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside…

Each sub-Riemannian geometry with bracket generating distribution enjoys a background structure determined by the distribution itself. At the same time, those geometries with constant sub-Riemannian symbols determine a unique Cartan…

The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) K\"ahler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil…

In this work, we propose a novel framework for defining the dual structure of a spinor. This construction relies on the basis elements of the Clifford algebra, leading to a covariant structure that embeds the dual. The formulation includes…