Classification of Spherical Nilpotent Orbits in Complex Symmetric Space | Synapse
March 29, 2026Open Access
Classification of Spherical Nilpotent Orbits in Complex Symmetric Space
Key Points
The aim is to classify spherical nilpotent orbits within the framework of complex symmetric spaces.
Utilized properties of the adjoint group of simple real Lie algebras
Analyzed isotropy representations at the identity coset
Applied theoretical frameworks related to symmetric spaces
Identified distinct classifications of nilpotent orbits
Proposed connections between orbits and associated group structures
Demonstrated the relevance of these classifications to broader mathematical theories
Abstract
Let G be the adjoint group of the simple real Lie algebra g, and let K C Aut(p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space.