On Lie-theoretic Hilbert schemesMPIM

by Oscar Kivinen (Aalto University)

Friday Sep 25, 2026, 2:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Oberseminar Representation Theory

There is a natural and representation-theoretically important class of varieties generalizing the Hilbert scheme of points on the plane, arising from a symbolic blow-up construction associated to a reductive Lie algebra. These varieties have twistor deformations to Calogero-Moser spaces and quantize to rational Cherednik algebras with equal parameters. Their fixed points are conjecturally in bijection with two-sided cells in the Weyl group. The natural trigonometric and elliptic generalizations of these varieties are closely related to unipotent orbits and Lusztig’s stratification of reductive groups. I will explain what is known about these varieties at present, including the resolution of the fixed-point conjecture outside type E, and pose some open questions.