Open Access
2016 Properties of Nilpotent Orbit Complexification
Peter Crooks
J. Gen. Lie Theory Appl. 10(S2): 1-6 (2016). DOI: 10.4172/1736-4337.1000S2-012


We consider aspects of the relationship between nilpotent orbits in a semisimple real Lie algebra $\mathfrak{g}$ and those in its complexification $\mathfrak{g}_{\mathbb{C}}$. In particular, we prove that two distinct real nilpotent orbits lying in the same complex orbit are incomparable in the closure order. Secondly, we characterize those $\mathfrak{g}$ having non-empty intersections with all nilpotent orbits in $\mathfrak{g}_{\mathbb{C}}$. Finally, for $\mathfrak{g}$ quasi-split, we characterize those complex nilpotent orbits containing real ones.


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Peter Crooks. "Properties of Nilpotent Orbit Complexification." J. Gen. Lie Theory Appl. 10 (S2) 1 - 6, 2016.


Published: 2016
First available in Project Euclid: 16 November 2016

zbMATH: 1371.17008
MathSciNet: MR3663981
Digital Object Identifier: 10.4172/1736-4337.1000S2-012

Keywords: KostantSekiguchi correspondence , nilpotent orbit , Quasi-split Lie algebra

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.10 • No. S2 • 2016
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