Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. S. K. Donaldson. Nahm's equations and the classification of monopoles. Comm. Math. Phys., 96:387-407, 1984. MR 86c:58039
  • 2. P. B. Kronheimer. A hyper-Kählerian structure on coadjoint orbits of a semisimple complex group. J. London Math. Soc., 42(2):193-208, 1990. MR 92b:53031
  • 3. P. B. Kronheimer. Instantons and the geometry of the nilpotent variety. J. Differential Geometry, 32:473-490, 1990. MR 91m:58021
  • 4. T. Ohta. The closures of nilpotent orbits in the classical symmetric pairs and their singularities. Tohoku Math. J., 43(2):161-211, 1991 MR 93c:22036
  • 5. J. Sekiguchi. Remarks on real nilpotent orbits of a symmetric pair. J. Math. Soc. Japan, 39:127-138, 1987. MR 88g:53053
  • 6. M. Vergne. Instantons et correspondence de Kostant-Sekiguchi, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), 901-906. MR 96c:22026

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 22E15, 17B05

Retrieve articles in all journals with MSC (1991): 22E15, 17B05

Additional Information

Dan Barbasch
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14850

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

Keywords: Konstant--Sekiguchi, nilpotent orbits
Received by editor(s): July 18, 1996
Communicated by: Roe Goodman
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society