Nilpotent cones and adjoint orbits

TL;DR

This paper proves that elements within the open cone associated with a nilpotent orbit on a period domain are all equivalent under the domain's symmetry group, revealing a symmetry property of these geometric structures.

Contribution

It demonstrates that the elements of the open cone underlying a nilpotent orbit are pairwise congruent under the symmetry group of the period domain, highlighting a new symmetry aspect.

Findings

Elements of the open cone are pairwise congruent under the symmetry group.

The result applies specifically to nilpotent orbits on period domains.

The paper provides a concise proof of this symmetry property.

Abstract

A short note to show that the elements of the (open) cone underlying a nilpotent orbit on a period domain are pairwise congruent under the symmetry group of the period domain.