Perverse sheaves and the cohomology of regular Hessenberg varieties

Autor:	Balibanu, Ana, Crooks, Peter
Rok vydání:	2020
Předmět:	Mathematics - Representation Theory Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	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." Comment: Final version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.07970 Zobrazit plný text záznamu View this record from Arxiv