Accessibility of Nilpotent Orbits in Classical Algebras

2021/06/12 by Luuk Jan-Paul Disselhorst, Disselhorst, Luuk
Mathematics · #14L35 (Secondary) #20G15 (Primary) 14L24 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2106.06810

openalex publication_date 2021/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a classical linear algebraic group over an algebraically closed field, and let \mathfrakn denote the subset of nilpotent elements in its Lie algebra. In this paper we study a partial order on the G-orbits in \mathfrakn given by taking limits along cocharacters of G. This gives rise to the so-called accessibility order on the nilpotent orbits. Our main results show that for general and special linear algebras, this new order coincides with the usual dominance order on nilpotent orbits, but for symplectic and orthogonal algebras this is not the case.

Related

• Computing with nilpotent orbits in simple Lie algebras of exceptional type
• Nilpotent orbits in classical Lie algebras over F_2ⁿ and the Springer correspondence
• General Linear and Symplectic Nilpotent Orbit Varieties
• Defining Equations of Nilpotent Orbits for Borel Subgroups of Modality Zero in Type A_n
• Computations with nilpotent orbits in SLA