Perverse Sheaves and the Cohomology of Regular Hessenberg Varieties
Perverse Sheaves and the Cohomology of Regular Hessenberg Varieties
复制标题
DOI：
10.1007/s00031-022-09755-3
复制
发表时间：
2020-04
影响因子：
0.7
通讯作者：
Ana Bălibanu;Peter Crooks
中科院分区：
文献类型：
--
作者：
Ana Bălibanu;Peter Crooks
利用施普林格对应给出了正则半单Hessenberg变元上同调环上Weyl群的Tymoczko点作用中出现的不可约表示的部分刻画。在a型中，我们应用这些技术证明了在普遍的Hessenberg族上常轴的推进中出现的所有不可约和都是完全支持的。我们还注意到Brosnan和Chow将局部不变循环定理应用于a型正则Hessenberg变元族的最新结果，可以推广到任意Lie型。我们使用这个扩展来证明规则的Hessenberg变种，虽然不一定是光滑的，但总是有“Kähler包”。
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In typeA, we apply these techniques to prove that all irreducible summands which appear in the pushforward of the constant sheaf on the universal Hessenberg family have full support. We also observe that the recent results of Brosnan and Chow, which apply the local invariant cycle theorem to the family of regular Hessenberg varieties in typeA, extend to arbitrary Lie type. We use this extension to prove that regular Hessenberg varieties, though not necessarily smooth, always have the “Kähler package.”