Reality of Unipotent elements in Classical Lie Groups

TL;DR

This paper classifies real and strongly real unipotent elements in classical simple Lie groups by introducing an infinitesimal notion of classical reality, providing a new framework for understanding their structure.

Contribution

It introduces an infinitesimal concept of classical reality and applies it to classify unipotent elements in classical simple Lie groups, advancing the understanding of their structure.

Findings

Classification of real unipotent elements

Classification of strongly real unipotent elements

Introduction of an infinitesimal notion of classical reality

Abstract

The aim of this paper is to give a classification of real and strongly real unipotent elements in a classical simple Lie group. To do this, we will introduce an infinitesimal version of the notion of classical reality in a Lie group. This notion has been applied to classify real and strongly real unipotent elements in a classical simple Lie group.