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

TL;DR

This paper introduces an algorithm to compute the closure ordering of nilpotent orbits in $ heta$-representations, aiding the understanding of orbit structures in graded Lie algebras.

Contribution

It presents a novel algorithm specifically designed for calculating the closure of nilpotent orbits in $ heta$-representations derived from graded simple Lie algebras.

Findings

Algorithm effectively computes orbit closures

Applicable to $ heta$-representations from graded Lie algebras

Enhances understanding of nilpotent orbit structures

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 $\Z$ or a $\Z/m\Z$-grading $\g= \bigoplus \g_i$ of a simple complex Lie algebra $\g$.