论文标题
GKM理论的常规半神经赫森伯格品种的第二个共同体学
The second cohomology of regular semisimple Hessenberg varieties from GKM theory
论文作者
论文摘要
我们在GKM理论方面明确描述了生成器的常规半神经赫森伯格品种的第二个共同体学。常规的半圣赫森伯格品种的共同体成为对称组$ \ mathfrak {s} _n $的模块，由tymoczko引入的点动作。作为我们的明确描述的应用，我们给出了一个公式，将第二个同胞的同构类别描述为$ \ mathfrak {s} _n $ -module。我们的公式与Chow或Cho-Hong-Lee的已知公式并不完全相同，但它们是等效的。我们还讨论了其更高的概括。
We describe the second cohomology of a regular semisimple Hessenberg variety by generators and relations explicitly in terms of GKM theory. The cohomology of a regular semisimple Hessenberg variety becomes a module of a symmetric group $\mathfrak{S}_n$ by the dot action introduced by Tymoczko. As an application of our explicit description, we give a formula describing the isomorphism class of the second cohomology as an $\mathfrak{S}_n$-module. Our formula is not exactly the same as the known formula by Chow or Cho-Hong-Lee but they are equivalent. We also discuss its higher degree generalization.
