Journal of Lie Theory 25 (2015), No. 2, 507--533
Copyright Heldermann Verlag 2015
Smallest Complex Nilpotent Orbits with Real Points
Takayuki Okuda
Dept. of Mathematics, Graduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Japan 739-8526
okudatak@hiroshima-u.ac.jp
Let g be a non-compact real simple Lie algebra without complex structure, and denote by gC the complexification of g. This paper focuses on non-zero 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 Dynkin-Kostant 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
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