Properties of Nilpotent Orbit Complexification

Real and complex nilpotent orbits have received considerable attention in the literature. The former have been studied in a variety of contexts, including differential geometry, symplectic geometry, and Hodge theory.  Also, there has been some interest in concrete descriptions of the poset structure on real nilpotent orbits in specific cases. By contrast, complex nilpotent orbits are studied in algebraic geometry and representation theory — in particular, Springer Theory.

Attention has also been given to the interplay between real and complex nilpotent orbits, with the Kostant-Sekiguchi Correspondence being perhaps the most famous instance. Accordingly, the present article provides additional points of comparison between real and complex nilpotent orbits. Specifically, let g be a finite-dimensional semisimple real Lie algebra with complexification g Each real nilpotent orbit.