Real structures on nilpotent orbit closures

TL;DR

This paper classifies equivariant real structures on nilpotent orbit closures and their normalizations within complex semisimple Lie algebras, advancing understanding of their geometric and algebraic properties.

Contribution

It provides a complete classification of real structures on nilpotent orbits and their closures, a novel result in the study of Lie algebra orbit geometry.

Findings

Classification of equivariant real structures on nilpotent orbits

Determination of real structures on orbit closures and their normalizations

Enhanced understanding of orbit geometry in Lie algebra representations

Abstract

We determine the equivariant real structures on nilpotent orbits and the normalizations of their closures for the adjoint action of a complex semisimple algebraic group on its Lie algebra.