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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Nilpotent orbits and theta-stable parabolic subalgebras
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by Alfred G. Noël
Represent. Theory 2 (1998), 1-32
Published electronically: February 3, 1998


In this work, we present a new classification of nilpotent orbits in a real reductive Lie algebra ${\mathfrak {g}}$ 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 ${\mathfrak {p}}_{{}_{\mathbb {C}}}$, the “complex symmetric space associated with ${\mathfrak {g}}$”. The Kostant-Sekiguchi correspondence, a bijection between nilpotent orbits in ${\mathfrak {g}}$ and nilpotent orbits in ${\mathfrak {p}}_{{}_{\mathbb {C}}}$, is also used. We identify a fundamental set of noticed nilpotents in ${\mathfrak {p}}_{{}_{\mathbb {C}}}$ 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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Bibliographic Information
  • Alfred G. Noël
  • Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts, 02115; Peritus Software Services Inc. 304 Concord Road, Billerica, Massachusetts 01821
  • Email:,
  • 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.
  • © Copyright 1998 American Mathematical Society
  • Journal: Represent. Theory 2 (1998), 1-32
  • MSC (1991): Primary 17B20, 17B70
  • DOI:
  • MathSciNet review: 1600330