Nilpotent orbits and theta-stable

parabolic subalgebras

Author:
Alfred G. Noël

Journal:
Represent. Theory **2** (1998), 1-32

MSC (1991):
Primary 17B20, 17B70

DOI:
https://doi.org/10.1090/S1088-4165-98-00038-7

Published electronically:
February 3, 1998

MathSciNet review:
1600330

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this work, we present a new classification of nilpotent orbits in a real reductive Lie algebra under the action of its adjoint group. Our classification generalizes the Bala-Carter classification of the nilpotent orbits of complex semisimple Lie algebras. Our theory takes full advantage of the work of Kostant and Rallis on , the ``complex symmetric space associated with ''. The Kostant-Sekiguchi correspondence, a bijection between nilpotent orbits in and nilpotent orbits in , is also used. We identify a fundamental set of *noticed* nilpotents in and show that they allow us to recover all other nilpotents. Finally, we study the behaviour of a principal orbit, that is an orbit of maximal dimension, under our classification. This is not done in the other classification schemes currently available in the literature.

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Additional Information

**Alfred G. Noël**

Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts, 02115;
Peritus Software Services Inc. 304 Concord Road, Billerica, Massachusetts 01821

Email:
anoel@lynx.neu.edu, anoel@peritus.com

DOI:
https://doi.org/10.1090/S1088-4165-98-00038-7

Keywords:
Parabolic subalgebras,
nilpotent orbits,
reductive Lie algebras

Received by editor(s):
August 11, 1997

Received by editor(s) in revised form:
December 3, 1997

Published electronically:
February 3, 1998

Additional Notes:
The author thanks his advisor, Donald R. King, for his helpful suggestions.

Article copyright:
© Copyright 1998
American Mathematical Society