Smallest Complex Nilpotent Orbits with Real Points
Journal of Lie Theory, Tome 25 (2015) no. 2, pp. 507-533
Voir la notice de l'article provenant de la source Heldermann Verlag
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.
Classification :
17B08, 17B20, 17B22
Mots-clés : Nilpotent orbit, real simple Lie algebra
Mots-clés : Nilpotent orbit, real simple Lie algebra
Affiliations des auteurs :
Takayuki Okuda 1
Takayuki Okuda. Smallest Complex Nilpotent Orbits with Real Points. Journal of Lie Theory, Tome 25 (2015) no. 2, pp. 507-533. http://geodesic.mathdoc.fr/item/JOLT_2015_25_2_a10/
@article{JOLT_2015_25_2_a10,
author = {Takayuki Okuda},
title = {Smallest {Complex} {Nilpotent} {Orbits} with {Real} {Points}},
journal = {Journal of Lie Theory},
pages = {507--533},
year = {2015},
volume = {25},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_2_a10/}
}