Parabolic Hilbert schemes and representation theory

Abstract: 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.

algebraic geometry

Audience: researchers in the topic

UC Davis algebraic geometry seminar