Closure ordering and the Kostant-Sekiguchi correspondence

Barbasch, Dan; Sepanski, Mark

doi:10.1090/S0002-9939-98-04090-8

Closure ordering and the Kostant-Sekiguchi correspondence
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by Dan Barbasch and Mark R. Sepanski

Proc. Amer. Math. Soc. 126 (1998), 311-317

DOI: https://doi.org/10.1090/S0002-9939-98-04090-8

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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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