论文标题
普通的赫森伯格品种的不良滑轮和共同学
Perverse sheaves and the cohomology of regular Hessenberg varieties
论文作者
论文摘要
我们使用Springer对应关系来对Weyl群的Tymoczko点效应出现在常规半神经Hessenberg品种的共同体学环上。在A型中，我们应用了这些技术来证明在通用Hessenberg家族的不断捆绑中出现的所有不可还原的求和都具有全部支持。我们还观察到，Brosnan和Chow的最新结果将局部不变循环定理应用于A型的常规Hessenberg品种的家族，扩展到任意谎言类型。我们使用此扩展名来证明常规的Hessenberg品种虽然不一定光滑，但总是具有“ Kahler软件包”。
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 type A, 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 type A, extend to arbitrary Lie type. We use this extension to prove that regular Hessenberg varieties, though not necessarily smooth, always have the "Kahler package."
