
Journal of Lie Theory 25 (2015), No. 2, 507533 Copyright Heldermann Verlag 2015 Smallest Complex Nilpotent Orbits with Real Points Takayuki Okuda Dept. of Mathematics, Graduate School of Science, Hiroshima University, 131 Kagamiyama, HigashiHiroshima, Japan 7398526 okudatak@hiroshimau.ac.jp Let g be a noncompact real simple Lie algebra without complex structure, and denote by gC the complexification of g. This paper focuses on nonzero nilpotent adjoint orbits in gC meeting g. We show that the poset consisting of such nilpotent orbits equipped with the closure ordering has the minimum O. Furthermore, we determine such O in terms of the DynkinKostant classification even in the cases where O does not coincide with the minimal nilpotent orbit in gC. We also prove that the intersection of g and O is the union of all minimal nilpotent orbits in g. Keywords: Nilpotent orbit, real simple Lie algebra. MSC: 17B08; 17B20, 17B22 [ Fulltextpdf (502 KB)] for subscribers only. 