Abundance of nilpotent orbits in real semisimple Lie algebras

2016/12/09 by Takayuki Okuda, Okuda, Takayuki
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Primary 17B08 #Representation Theory (math.RT) #Secondary 57S30

paper · pdf · doi:10.48550/arxiv.1612.02896

openalex publication_date 2016/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate and prove that there are "abundant" in nilpotent orbits in real semisimple Lie algebras, in the following sense. If S denotes the collection of hyperbolic elements corresponding the weighted Dynkin diagrams coming from nilpotent orbits, then S span the maximally expected space, namely, the (-1)-eigenspace of the longest Weyl group element. The result is used to the study of fundamental groups of non-Riemannian locally symmetric spaces.

Related

• Approximation of nilpotent orbits for simple Lie groups
• Series of nilpotent orbits
• Computing with nilpotent orbits in simple Lie algebras of exceptional type
• Homotopy type of the nilpotent orbits in classical Lie algebras
• Real Structures on Nilpotent Orbit Closures