Mitosis recursion for coefficients of Schubert polynomials

Mitosis algorithm for Grothendieck polynomials

In this article we will introduce the way to extend the mitosis algorithm for Schubert polynomials, developed by Ezra Miller, to the case of Grothendieck polynomials.

带滤子和递归的Schubert模块

Filtrations and recursions for Schubert modules

本文通过重新审视Kraśkiewicz和Pragacz的构造，提供了一个新的证明，表明其特征等于Schubert多项式。主要创新是用表示论解释了Nadeau、Spink和Tewari最近发现的Schubert多项式递归关系。

A combinatorial rule for (co)minuscule Schubert calculus

We prove a root system uniform, concise combinatorial rule for Schubert calculus of_minuscule_ and_cominuscule_ flag manifolds G/P (the latter are also known as "compact Hermitian symmetric spaces"). We connect this geometry to the poset combinatorics of [Proctor '04], thereby giving a generalization of the [Schützenberger `77]_jeu de taquin_ formulation of the Littlewood-Richardson rule that computes the intersection numbers of Grassmannian Schubert varieties. Our proof introduces_cominuscule recursions_, a general technique to relate the numbers for different Lie types. A discussion about co…

Gröbner geometry of Schubert polynomials

Our main theorems provide a single geometric setting in which polynomial representatives for Schubert classes in the integral cohomology ring of the flag manifold are determined uniquely, and have positive coefficients for geometric reasons. This results in a geometric explanation for the naturality of Schubert polynomials and their associated combinatorics. Given a permutation w in S_n, we consider a determinantal ideal I_w whose generators are certain minors in the generic n x n matrix (filled with independent variables). Using `multidegrees' as simple algebraic substitutes for torus-equivar…