Some remarks on Richardson orbits in complex symmetric spaces
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- by Alfred G. Noël;
- Math. Comp. 75 (2006), 395-417
- DOI: https://doi.org/10.1090/S0025-5718-05-01784-9
- Published electronically: September 29, 2005
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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.References
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Bibliographic Information
- Alfred G. Noël
- Affiliation: Mathematics Department, The University of Massachusetts, Boston, Massachusetts 02125-3393
- Email: anoel@math.umb.edu
- 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.
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 75 (2006), 395-417
- MSC (2000): Primary 17B05, 17B10, 17B20, 22E30
- DOI: https://doi.org/10.1090/S0025-5718-05-01784-9
- MathSciNet review: 2176406