Speaker：Jiayu Huang（The Chinese University of Hong Kong, Shenzhen）

Time：2022-12-01, 15:00

Location：Tencent Meeting ID：685-688-558（No Password）

Abstract:

Let G be a complex classical group treated as a real group. For any nilpotent varieties (Zariski closure of nilpotent orbits) of G, Ranee Brylinski constructed a Dixmier algebra whose K-spectrum matches with its ring of regular functions.

In this talk, we will investigate and understand Brylinski's model using (i) Howe's dual pair correspondence, (ii) deformation quantization of nilpotent orbits by Losev-Mason-Brown-Matvieievski, and (iii) singularities of nilpotent varieties, resulting in a better understanding on the (non)-normality of these varieties. Under this perspective, we give a conjecture on the structure of regular functions for non-normal exceptional nilpotent varieties with branched singularities.

This is a joint work with Dan Barbasch.