布尔舒伯特结构系数

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-10-10 DOI:10.1016/j.jalgebra.2025.09.024

Yibo Gao , Hai Zhu

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引用次数: 0

摘要

Schubert问题要求用组合模型来计算关于Schubert类的上同环的结构常数，是代数几何和组合学中的一个重要开放问题，几十年来指导了卓有成效的研究。本文给出了当元素u，v，w为布尔值时，所有Lie类型的（等变）Schubert结构常数cuvw的显式公式。特别地，在类型A中，布尔元素上的所有Schubert结构常数要么为0，要么为1。

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Boolean Schubert structure coefficients

The Schubert problem asks for combinatorial models to compute structure constants of the cohomology ring with respect to Schubert classes and has been an important open problem in algebraic geometry and combinatorics that guided fruitful research for decades. In this paper, we provide an explicit formula for the (equivariant) Schubert structure constants

c_{u v}^{w}

across all Lie types when the elements

u, v, w

are boolean. In particular, in type A, all Schubert structure constants on boolean elements are either 0 or 1.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.