Abundance of nilpotent orbits in real semisimple Lie algebras

T Okuda - arXiv preprint arXiv:1612.02896, 2016 - arxiv.org
T Okuda
arXiv preprint arXiv:1612.02896, 2016arxiv.org
We formulate and prove that there are" abundant" in nilpotent orbits in real semisimple Lie
algebras, in the following sense. If S denotes the collection of hyperbolic elements
corresponding the weighted Dynkin diagrams coming from nilpotent orbits, then S span the
maximally expected space, namely, the (-1)-eigenspace of the longest Weyl group element.
The result is used to the study of fundamental groups of non-Riemannian locally symmetric
spaces.
We formulate and prove that there are "abundant" in nilpotent orbits in real semisimple Lie algebras, in the following sense. If S denotes the collection of hyperbolic elements corresponding the weighted Dynkin diagrams coming from nilpotent orbits, then S span the maximally expected space, namely, the (-1)-eigenspace of the longest Weyl group element. The result is used to the study of fundamental groups of non-Riemannian locally symmetric spaces.
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