Abundance of Nilpotent Orbits in Real Semisimple Lie Algebras
Vol. 24 (2017), No. 3, Page 399-430.
Okuda, Takayuki
Abundance of Nilpotent Orbits in Real Semisimple Lie Algebras
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Abstract:
We formulate and prove that nilpotent orbits are “abundant” 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 $S$ spans 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.
Keywords: Nilpotent orbit, weighted Dynkin diagram, Satake diagram, Dynkin--Kostant classification
Mathematics Subject Classification (2010): Primary 17B08; Secondary 57S30
Mathematical Reviews Number: MR3700488
Received: 2016-12-09
