Hessenberg varieties and the geometric modular law

Abstract: Hessenberg varieties are fibers of certain proper maps to a simple Lie algebra. These maps are generalizations of the Springer and Grothendieck-Springer resolutions. In this talk, we describe some new properties of nilpotent Hessenberg varieties. In particular, we show that their cohomology satisfies a modular law as we vary the maps. This law generalizes one of De Concini, Lusztig, and Procesi and coincides with a combinatorial law of Guay-Paquet and Abreu-Nigro in type A. We also study the push-forward of the constant sheaf of these maps and show that only intersection cohomology sheaves with local systems coming from the Springer correspondence appear in the decomposition, resolving a conjecture of Brosnan. This is joint work with Martha Precup.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.