论文标题
常规半圣赫森伯格品种的统一同居的基础
Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties
论文作者
论文摘要
我们考虑了常规半神经赫森伯格品种的共同体学空间的基础，这些品种由hessenberg品种的bialynicki-birula分解自然产生的类别组成。我们对每个类的支持进行了明确的组合描述，这使我们能够计算基地中类上的对称组动作。然后，我们成功地将结果应用于置换式辅助品种，以明确写下每个类别，并构建构成每个程度共同分解空间分解的汇总子模块。这解决了Stembridge对置换模块分解的几何结构所带来的问题，以及Chow对置换品品种的均值同生体空间的基础构建所提出的猜想。
We consider bases for the cohomology space of regular semisimple Hessenberg varieties, consisting of the classes that naturally arise from the Bialynicki-Birula decomposition of the Hessenberg varieties. We give an explicit combinatorial description of the support of each class, which enables us to compute the symmetric group actions on the classes in our bases. We then successfully apply the results to the permutohedral varieties to explicitly write down each class and to construct permutation submodules that constitute summands of a decomposition of cohomology space of each degree. This resolves the problem posed by Stembridge on the geometric construction of permutation module decomposition and also the conjecture posed by Chow on the construction of bases for the equivariant cohomology spaces of permutohedral varieties.
