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We formulate and prove that there are "abundant" in nilpotent orbits in realsemisimple Lie algebras, in the following sense. If S denotes the collection ofhyperbolic elements corresponding the weighted Dynkin diagrams coming fromnilpotent orbits, then S span the maximally expected space, namely, the(-1)-eigenspace of the longest Weyl group element. The result is used to thestudy of fundamental groups of non-Riemannian locally symmetric spaces.

Abundance of nilpotent orbits in real semisimple Lie algebras