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Some remarks on Richardson orbits in complex symmetric spaces
Author(s):
Alfred
G.
Noël.
Journal:
Math. Comp.
75
(2006),
395-417.
MSC (2000):
Primary 17B05, 17B10, 17B20, 22E30
Posted:
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:
-
- 1.
- R. Carter, Simple Groups of Lie Type, Wiley Classics Library, John Wiley & Sons, London, 1989. MR 1013112 (90g:20001)
- 2.
- A. W. Knapp, Lie Groups Beyond an Introduction, Second Edition, Progr. Math., Birkhäuser, Boston, 140 2002. MR 1920389 (2003c:22001)
- 3.
- G. Lusztig and N. Spaltenstein, Induced unipotent classes, J. London Math. Soc. 19 (1979), 41-52. MR 0527733 (82g:20070)
- 4.
- A. G. Noël, Computing theta-stable parabolic subalgebras using LiE, Lecture Notes Comput. Sci., Springer-Verlag 3039 (2004), 335-342.
- 5.
- R. W. Richardson, Conjugacy classes in parabolic subgroups of semisimple algebraic groups, Bull. London Math. Soc. 6 (1974), 21-24. MR 0330311 (48:8648)
- 6.
- J. Sekiguchi, Remarks on real nilpotent orbits of a symmetric pair, J. Math. Soc. Japan 39, No. 1 (1987), 127-138. MR 0867991 (88g:53053)
- 7.
- P. Tauvel, Quelques résultats sur les algèbres de Lie symétriques, Bull. Sci. Math. 125 No. 8 (2001), 641-665. MR 1872599 (2002j:17008)
- 8.
- P. Trapa, Richardson orbits for real classical groups, J. Algebra 286 (2005), 361-385. MR 2128022
- 9.
- E. B. Vinberg, On the classification of the nilpotent elements of graded Lie algebras, Dokl. Acad. Nauk SSSR 225 (1975b), 745-748 (Russian). English translation: Soviet Math. Doklady 16 (1975), 1517-1520. MR 0506488 (58:22194)
- 10.
- M. A. A. Van Leeuwen, A. M. Cohen, and B. Lisser, LiE A package for Lie Group Computations, Computer Algebra Nederland, Amsterdam, The Netherlands (1992).
- 11.
- D. Djokovic Classification of nilpotent elements in simple exceptional real Lie algebras of inner type and description of their centralizers, J. Algebra 112 (1987) 577-585. MR 0926619 (89b:17010)
- 12.
- D. Djokovic, Classification of nilpotent elements in simple real Lie algebras
 and  and description of their centralizers, J. Algebra 116 (1988) 196-207. MR 0944155 (89k:17022)
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Additional Information:
Alfred
G.
Noël
Affiliation:
Mathematics Department, The University of Massachusetts, Boston, Massachusetts 02125-3393
Email:
anoel@math.umb.edu
DOI:
10.1090/S0025-5718-05-01784-9
PII:
S 0025-5718(05)01784-9
Keywords:
Parabolic group,
nilpotent orbits,
prehomogeneous spaces
Received by editor(s):
March 15, 2004
Posted:
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 of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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