Weighted Vogan diagrams associated to real nilpotent orbits

TL;DR

This paper introduces weighted Vogan diagrams to classify nilpotent orbits in real semisimple Lie algebras, providing a new combinatorial tool for understanding their structure.

Contribution

It characterizes weighted Vogan diagrams associated with noticed nilpotent elements, linking diagram features to orbit classification.

Findings

Weighted Vogan diagrams encode nilpotent orbit data.

Characterization criteria for diagrams of noticed nilpotent elements.

Enhanced understanding of orbit classification via combinatorial diagrams.

Abstract

We associate to each nilpotent orbit of a real semisimple Lie algebra $g_o$ a weighted Vogan diagram, that is a Dynkin diagram with an involution of the diagram, a subset of painted nodes and a weight for each node. Every nilpotent element of $g_o$ is noticed in some subalgebra of $g_o$. In this paper we characterize the weighted Vogan diagrams associated to orbits of noticed nilpotent elements.