Computing representatives of nilpotent orbits of theta-groups

TL;DR

This paper introduces two algorithms for computing representatives of nilpotent orbits in theta-groups, implemented in GAP, and applies them to study orbits in exceptional Lie algebras.

Contribution

The paper presents novel algorithms for nilpotent orbit representatives in theta-groups and demonstrates their implementation and application to exceptional Lie algebras.

Findings

Algorithms successfully compute nilpotent orbit representatives

Implementation in GAP enhances computational efficiency

Application to exceptional Lie algebras reveals new orbit structures

Abstract

We describe two algorithms for finding representatives of the nilpotent orbits of a theta-group. The algorithms have been implemented in the computer algebra system GAP (inside the package SLA). We comment on their performance. We apply the algorithms to study the nilpotent orbits of theta-groups, where theta is an N-regular automorphism of a simple Lie algebra of exceptional type.