Component Groups of Centralizers of Nilpotents in Complex Symmetric Spaces

Abstract Let G be the adjoint group of a simple Lie algebra g , and let K C  → Aut( p C ) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. If e  ∈  p C is nilpotent, we consider the centralizer of e in K C . We show that the conjugacy classes of the component group of this centralizer can be described in terms generalizing the Bala–Carter classification of nilpotent orbits in the complexification of g .