Journal of Generalized Lie Theory and Applications

Properties of Nilpotent Orbit Complexification

Peter Crooks

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Abstract

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

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

Dates
First available in Project Euclid: 16 November 2016

Permanent link to this document
https://projecteuclid.org/euclid.jglta/1479265231

Digital Object Identifier
doi:10.4172/1736-4337.1000S2-012

Zentralblatt MATH identifier
1371.17008

Keywords
Nilpotent orbit Quasi-split Lie algebra KostantSekiguchi correspondence

Citation

Crooks, Peter. Properties of Nilpotent Orbit Complexification. J. Gen. Lie Theory Appl. 10 (2016), no. S2, pages. doi:10.4172/1736-4337.1000S2-012. https://projecteuclid.org/euclid.jglta/1479265231


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