Lie Groups Seminar

Daniel WongCornell University
On the Kraft-Procesi model of classical nilpotent varieties

Friday, October 6, 2017 - 3:30pm
Malott 406

Let $G$ be a complex classical simple Lie group with Lie algebra $\mathfrak{g}$. The normal nilpotent varieties of $\mathfrak{g}$ were classified by Kraft and Procesi in the early 1980s. However, very little is known about the ring of regular functions of such varieties. Based on the work of Kraft-Procesi, a quantization model of classical nilpotent varieties was given by Ranee Brylinski in 2003. We study the representation theoretic perspective of the Brylinski model, which results in an explicit description on the ring of regular functions of classical nilpotent varieties in terms of the multiplicities of the irreducible, finite-dimensional representations of $G$.