|
Classification of admissible nilpotent orbits in simple exceptional real Lie algebras of inner type
Author(s):
Alfred
G.
Noël
Journal:
Represent. Theory
5
(2001),
455-493.
MSC (2000):
Primary 17B20, 17B70
Posted:
November 9, 2001
MathSciNet review:
1870598
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we give a classification of admissible nilpotent orbits of the noncompact simple exceptional real Lie groups of inner type. We use a lemma of Takuya Ohta and some information from the work of Dragomir Djokovic to construct a simple algorithm which allows us to decide the admissiblity of a given orbit.
References:
-
- [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).
- [C]
-
C. W. Curtis, Corrections and additions
to: `On the degrees
and rationality of certain characters of finite
Chevalley groups', Trans.
Amer. Math. Soc. 202 (1975),
405-406. MR
51:737
- [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 exceptional real Lie algebras of inner
type and description of their
centralizers, J. Alg. 112
(1987), 503-524. MR
89b:170
- [D2]
-
D. Djokovic, Proof of a conjecture of
Kostant,
Trans. Amer. Math. Soc. 302(2)
(1988), 577-585. MR
88j:17007
- [Dy]
-
E. Dynkin, Semisimple subalgebras of
simple Lie
algebras, Selected papers of E.B. Dynkin
with commentary edited by
Yushkevich, Seitz and Onishchik AMS, (2000), 175-309.
- [Dy1]
-
E. Dynkin, Semisimple subalgebras of
simple Lie
algebras, Amer. Soc. Transl. Ser. 2
6, (1957), 111-245.
- [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, Birkhäuser,
Progress in Mathematics Boston, 1996.
MR
98b:22002
- [Ne]
-
M. Nevins, Admissible nilpotent coadjoint
orbits in the
p-adic reductive groups, Ph.D. Thesis
M.I.T. Cambridge, MA (June 1998).
- [L]
-
G. Lusztig, Some problems in the representation
theory of
finite Chevalley groups, Proc. Symp.
Pure Math., 37,
Amer. Math. Soc., (1980), 313-317. MR
82i:20014
- [No]
-
A. G. Noël, Nilpotent orbits
and theta-stable
parabolic Subalgebras, Amer. Math.
Soc., J. Representation Theory 2,
(1998),
1-32. MR
99g:17023
- [No2]
-
A. G. Noël, Classification
of admissible nilpotent
orbits in simple real Lie algebras
 and
 ,
Amer. Math. Soc., J. Represent. Theory 5 (2001), 494-502.
- [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). MR
88g:53053
- [Se]
-
J. Sekiguchi, Remarks on real nilpotent
orbits of a
symmetric pair, J. Math. Soc. Japan
39, No. 1 (1987), 127-138.
- [S-S]
-
T. A. Springer and R. Steinberg, Conjugacy classes,
Seminar on Algebraic
Groups and Related Finite Groups, Lecture
Notes in Mathematics 131
(1970). MR
42:3091
- [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
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
Email:
alfred.noel@umb.edu
DOI:
10.1090/S1088-4165-01-00141-8
PII:
S 1088-4165(01)00141-8
Keywords:
Admissible,
nilpotent orbits,
reductive Lie algebras
Received by editor(s):
April 5, 2001
Received by editor(s) in revised form:
September 28, 2001
Posted:
November 9, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
|
