Journal of Generalized Lie Theory and Applications

Properties of Nilpotent Orbit Complexification

Peter Crooks

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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.

Article information

J. Gen. Lie Theory Appl., Volume 10, Number S2 (2016), pages.

First available in Project Euclid: 16 November 2016

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Zentralblatt MATH identifier

Nilpotent orbit Quasi-split Lie algebra KostantSekiguchi correspondence


Crooks, Peter. Properties of Nilpotent Orbit Complexification. J. Gen. Lie Theory Appl. 10 (2016), no. S2, pages. doi:10.4172/1736-4337.1000S2-012.

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