# Orbit closures in the enhanced nilpotent cone

Let $\mathcal N$ denote the set of $n \times n$ nilpotent matrices. The enhanced nilpotent cone’’ is the space $\mathbb C^n \times \mathcal N$. $GL(n)$ acts on $\mathbb C^n$ in an obvious way, and on $\mathcal N$ by conjugation. The orbits of this action are the subject of this talk. From this surprisingly elementary starting point, I will discuss connections to various topics in representation theory, combinatorics, and algebraic geometry, and especially to Syu Kato’s work on the exotic nilpotent cone’’ and affine Hecke algebras. This is joint work with A. Henderson.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.