Zeitschrift für verallgemeinerte Lügentheorie und -anwendungen

Properties of Nilpotent Orbit Complexification

Abstract

Peter Crooks

We consider aspects of the relationship between nilpotent orbits in a semisim-ple real Lie algebra g and those in its complexification g�. In particular, we prove that two distinct real nilpotent orbits lying in the same complex orbit are incomparable in the closure order. Secondly, we characterize those g having non-empty intersections with all nilpotent orbits in g�. Finally, for g quasi-split, we characterize those complex nilpotent orbits containing real ones.