正则半单Hessenberg簇中Hessenberg Schubert簇的环面不动点集
代数几何
2022-02-09 v2 组合数学
摘要
众所周知，旗簇GL_n(C)/B中Schubert簇的T-不动点可以纯粹组合地用对称群S_n上的Bruhat序来刻画。在最近的一篇预印本中，Cho、Hong和Lee给出了正则半单Hessenberg簇中Schubert簇的Hessenberg类比（我们称之为Hessenberg Schubert簇）的T-不动点的组合描述。本文笔记利用通过所谓Weyl型子集定义的对称群的一个划分，从Bruhat序的角度对其结果给出了解释。由Michael Zeng撰写的附录证明了我们论证中所需要的关于Weyl型子集的一个引理。
引用
@article{arxiv.2112.13250,
title = {Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties},
author = {Megumi Harada and Martha Precup},
journal= {arXiv preprint arXiv:2112.13250},
year = {2022}
}
备注
13 pages. Major revision, due to an error discovered in the proof of the main theorem of the previous version. The current version states and proves a revised result, which concerns the T-fixed points of the Hessenberg Schubert variety instead of the variety itself