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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Closure ordering
and the Kostant-Sekiguchi correspondence


Authors: Dan Barbasch and 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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Additional Information

Dan Barbasch
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850
Email: barbasch@math.cornell.edu

Mark R. Sepanski
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Address at time of publication: Department of Mathematics, Baylor University, Waco, Texas 76798-7328
Email: Mark_Sepanski@Baylor.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04090-8
PII: S 0002-9939(98)04090-8
Keywords: Konstant--Sekiguchi, nilpotent orbits
Received by editor(s): July 18, 1996
Communicated by: Roe Goodman
Article copyright: © Copyright 1998 American Mathematical Society