Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra

Abstract: In this note we give an alternative presentation of the rational Cherednik algebra $H_c$ corresponding to the permutation representation of $S_n$. As an application, we give an explicit combinatorial basis for all standard and simple modules if the denominator of $c$ is at least $n$, and describe the action of $H_c$ in this basis. We also give a basis for the irreducible quotient of the polynomial representation and compare it to the basis of fixed points in the homology of the parabolic Hilbert scheme of points on the plane curve singularity $\{x^n=y^m\}$. This is a joint work with José Simental and Monica Vazirani.

mathematical physicsalgebraic geometryrepresentation theory

Audience: researchers in the topic

Geometric Representation Theory conference

Series comments: Originally planned as a twinned conference held simultaneously at the Max Planck Institute in Bonn, Germany and the Perimeter Institute in Waterloo, Canada. The concept was motivated by the desire to reduce the environmental impact of conference travels. In order to view the talks, register at the website: www.mpim-bonn.mpg.de/grt2020 . The talks from previous days can be be viewed at pirsa.org/C20030 ; slides from the talks are posted here: www.dropbox.com/sh/cjzqbqn7ql8zcjv/AAANB82Hh4t5XDc5RPcZzW0Aa?dl=0