Journal of Lie Theory

no. 2
Smallest Complex Nilpotent Orbits with Real Points
Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 507-533
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.
DOI: 10.5802/jolt.848
Classification: 17B08, 17B20, 17B22
Keywords: Nilpotent orbit, real simple Lie algebra 
@article{JOLT_2015_25_2_a10,
     author = {T. Okuda},
     title = {Smallest {Complex} {Nilpotent} {Orbits} with {Real} {Points}},
     journal = {Journal of Lie Theory},
     pages = {507--533},
     year = {2015},
     volume = {25},
     number = {2},
     doi = {10.5802/jolt.848},
     zbl = {1368.17008},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.848/}
}
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%J Journal of Lie Theory
%D 2015
%P 507-533
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T. Okuda. Smallest Complex Nilpotent Orbits with Real Points. Journal of Lie Theory, Volume 25 (2015) no. 2, pp. 507-533. doi: 10.5802/jolt.848

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