### Algebraic Geometry Seminar, UC Davis

Jose Simental Rodriguez, UC Davis

Parabolic Hilbert schemes and representation theory

Organizer's time: 2020-10-14 11:00 America/Los_Angeles

Duration: 1 hour

We explicitly construct an action of type A rational Cherednik algebras and, more generally, quantized Gieseker varieties, on the equivariant homology of the parabolic Hilbert scheme of points on the plane curve singularity $C=\{x^m=y^n\}$ where $m$ and $n$ are coprime positive integers. We show that the representation we get is a highest weight irreducible representation and explicitly identify its highest weight. We will also place these results in the recent context of Coulomb branches and BFN Springer theory. This is joint work with Eugene Gorsky and Monica Vazirani.

Submitted by: Eugene Gorsky