Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



Classification of admissible nilpotent orbits in simple real Lie algebras $E_{6(6)}$ and $E_{6(-26)}$

Author: Alfred G. Noël
Journal: Represent. Theory 5 (2001), 494-502
MSC (2000): Primary 17B20, 17B70
Published electronically: November 9, 2001
MathSciNet review: 1870599
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper completes the classification of admissible nilpotent orbits of the noncompact simple exceptional real Lie algebras. The author has previoulsly determined such orbits for exceptional real simple Lie algebras of inner type. Here he uses the same techniques, with some modifications, to classify the admissible nilpotent orbits of $E_{6(6)}$and $E_{6(-26)}$ under their simply connected Lie groups.

References [Enhancements On Off] (What's this?)

  • [A-K] L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255-354. MR 45:2092
  • [Bo] N. Bourbaki, Groupes et Algèbre de Lie, Chapitres 4,5,6, Elements de mathématique. MASSON (1981). MR 39:1590
  • [D] M. Duflo, Construction de représentations unitaires d'un groupe de Lie, Harmonic Analysis and Group Representations. C.I.M.E. (1982). MR 87b:22028
  • [D1] D. Djokovic, Classification of nilpotent elements in simple real Lie algebras $E_{6(6)}$ and $E_{6(-26)}$ and description of their centralizers, J. Alg. 116 (1988), 196-207. MR 89k:17022
  • [D2] D. Djokovic, Explicit Cayley triples in real forms of $G_{2}$, $F_{4}$ and $E_{6}$, Pac. J. of Math. 184 (1998), 231-255. MR 99e:17005
  • [K] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Russian Math. Surveys 17 (1962), 57-110. MR 25:5396
  • [K-R] B. Kostant and S. Rallis, Orbits and representations associated with symmetric spaces, Amer. J. Math. 93 (1971), 753-809. MR 47:399
  • [Kn] A. W. Knapp, Lie Groups Beyond an Introduction, vol. 140, Progress in Mathematics, Birkhäuser Boston, Boston, 1996. MR 98b:22002
  • [Ku] J. F. Kurtzke, Centers of centralizers in reductive algebraic groups, Comm. Algebra 19 (1991), no. 12, 3393-3410. MR 92j:20043
  • [Ne] M. Nevins, Admissible nilpotent coadjoint orbits in the p-adic reductive groups, Ph. D. Thesis M.I.T. Cambridge, MA (June 1998).
  • [No] A. G. Noël, Nilpotent orbits and theta-stable parabolic subalgebras, Amer. Math. Soc., J. Represent. Theory 2, (1998), 1-32. MR 99g:17023
  • [No1] A. G. Noël, Classification of admissible nilpotent orbits in simple exceptional real Lie algebras of inner type, Amer. Math. Soc., J. Representation Theory 5 (2001), 455-493.
  • [O] T. Ohta, Classification of admissible nilpotent orbits in the classical real Lie algebras, J. of Algebra 136, No. 1 (1991), 290-333. MR 92j:22032
  • [Sch] J. Schwartz, The determination of the admissible nilpotent orbits in real classical groups, Ph.D. Thesis M.I.T. Cambridge, MA (1987).
  • [Se] J. Sekiguchi, Remarks on real nilpotent orbits of a symmetric pair, J. Math. Soc. Japan 39, No. 1 (1987), 127-138. MR 88g:53053
  • [V] D. Vogan, Jr., Unitary representations of reductive groups, Annals of Mathematical Studies, Princeton University Press Study 118 (1987). MR 89g:22024
  • [V1] D. Vogan, Jr., Associated varieties and unipotent representations, Harmonic Analysis on Reductive Groups (1991), 315-388. MR 93k:22012

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 17B20, 17B70

Retrieve articles in all journals with MSC (2000): 17B20, 17B70

Additional Information

Alfred G. Noël
Affiliation: Department of Mathematics, University of Massachusetts, Boston, Massachusetts 02125
Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Keywords: Admissible, nilpotent orbits, reductive Lie algebras
Received by editor(s): May 18, 2001
Received by editor(s) in revised form: August 17, 2001
Published electronically: November 9, 2001
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society