An effective method to compute closure ordering for nilpotent orbits of $\theta$-representations

Abstract

We develop an algorithm for computing the closure of a given nilpotent $G_0$-orbit in $\g_1$, where $\g_1$ and $G_0$ are coming from a $\mathbb{Z}$ or a $\mathbb{Z}/m\mathbb{Z}$-grading $\g= \bigoplus \g_i$ of a simple complex Lie algebra $\g$.