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Some remarks on Richardson orbits in complex symmetric spaces

Author: Alfred G. Noël
Journal: Math. Comp. 75 (2006), 395-417
MSC (2000): Primary 17B05, 17B10, 17B20, 22E30
Published electronically: September 29, 2005
MathSciNet review: 2176406
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Abstract: Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a theorem of Peter E. Trapa (in 2005) to real semisimple exceptional Lie groups.

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Additional Information

Alfred G. Noël
Affiliation: Mathematics Department, The University of Massachusetts, Boston, Massachusetts 02125-3393

Keywords: Parabolic group, nilpotent orbits, prehomogeneous spaces
Received by editor(s): March 15, 2004
Published electronically: September 29, 2005
Additional Notes: The author was partially supported by an NSF research opportunity award sponsored by David Vogan of MIT. He thanks him for the support. The author is also grateful to Donald R. King and Peter E. Trapa for several discussions about the content of this paper. Finally, he expresses his thanks to the referee for his kind words.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.