Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Closure ordering and the Kostant-Sekiguchi correspondence

Author(s): Dan Barbasch; Mark R. Sepanski
Journal: Proc. Amer. Math. Soc. 126 (1998), 311-317.
MSC (1991): Primary 22E15, 17B05
MathSciNet review: 1422847
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Abstract: Let $S$ be a real semisimple Lie group with Lie algebra $\mathfrak{s}=\mathfrak{k} +\mathfrak{p}$ . The Kostant-Sekiguchi correspondence is a bijection between nilpotent $S$ orbits on $\mathfrak{s}$ and nilpotent $K_{\mathbb{C}}$ orbits on $\mathfrak{p}_{\mathbb{C}}$ . In this note we prove that the closure relations among nilpotent orbits are preserved under the Kostant-Sekiguchi correspondence. The techniques rely on work of M. Vergne and P. Kronheimer.

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