Electronic Only Electronic Research Announcements
Representation Theory
ISSN 1088-4165
Previous volume | Table of contents | Next volume
Articles in press | Most recent volume | All volumes
Previous Article | Next Article
     

Minimal representations of exceptional $p$-adic groups

Author(s): Karl E. Rumelhart
Journal: Represent. Theory 1 (1997), 133-181.
MSC (1991): Primary 22E35, 22E50, 17B25, 17B60; Secondary 11F70, 11F27, 17C50
Posted: June 19, 1997
Retrieve article in: PDF
This article is available free of charge

References | Similar articles | Additional information

References:

[B-K]
R. Brylinski and B. Kostant, `Lagrangian models of minimal representations of $E_6$, $E_7$ and $E_8$.' In Functional Analysis on the Eve of the 21st Century, in honor of I. M. Gelfand, Progress in Math. 131, Birkhäuser, 1995, pp. 13-63. MR 96m:22025

[C-M]
D. Collingwood and W. McGovern, Nilpotent Orbits in Semisimple Lie Algebras, Van Nostrand Reinhhold, 1993. MR 94j:17001

[F]
H. Freudenthal, `Beziehungen der $E_7$ and $E_8$ zur Oktavenebene, I, II.' Nederl. Akad. Wetensch. Proc. A 57 (1954), pp. 133-181, 363-368. MR 16:900d; MR 16:108b

[G-W]
B. Gross and N. Wallach, `A distinguished family of unitary representations for the exceptional groups of real rank=4.' In Lie Theory and Geometry, in honor of Bertram Kostant, Progress in Math. 123, Birkhäuser, 1994, pp. 289-304. MR 96i:22034

[H-C]
Harish-Chandra, `Admissible invariant distributions on reductive $p$-adic groups.' Queens Papers in Pure and Applied Math., 48 (1978), pp. 133-181. MR 58:28313

[H1]
R. Howe, `Kirillov theory for compact $p$-adic groups.' Pacific J. Math. 73 (1977), pp. 133-181. MR 58:28314

[H2]
R. Howe, `Topics in harmonic analysis on solvable algebraic groups.' Pacific J. Math. 73 (1977), pp. 383-435. MR 58:1007

[J]
N. Jacobson, Structure and Representations of Jordan Algebras. Amer. Math. Soc., Providence, Rhode Island, 1968. MR 40:4330

[K]
D. Kazhdan, `The minimal representation of $D_4$.' In Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, in honor of Jacques Dixmier, Progress in Math. 92, Birkhäuser, 1990, pp. 125-158. MR 92i:22015

[K-S]
D. Kazhdan and G. Savin, `The smallest representation of simply laced groups.' In Israel Math. Conference Proceedings, Piatetski-Shapiro Festschrift 2, 1990, pp. 209-233. MR 93f:22019

[Ko]
M. Koecher, `Imbedding of Jordan algebras into Lie algebras.' Amer. J. Math. 89 (1967), pp. 133-181. MR 35:5480

[Ma]
H. Matsumoto, `Sur les sous-groupes arithmétiques des groups semi-simples déployés.' Ann. Scient. Ec. Norm. Sup. 2 (1969), pp. 133-181. MR 39:1566

[M-V-W]
C. Moeglin, M.-F. Vignéras and J.-L. Waldspurger, Correspondances de Howe sur un corps p-adique, Lecture Notes in Math. 1291, Springer-Verlag, 1987. MR 91f:11040

[M-W]
C. Moeglin and J.-L. Waldspurger, `Modèles de Whittaker dégénérés pour des groupes $p$-adiques.' Math. Zeitschrift 196 (1987), pp. 133-181. MR 89f:22024

[Pl-R]
V. Platonov and A. Rapinchuk, Algebraic Groups and Number Theory, Academic Press, 1994. MR 95b:11039

[Pr-R]
G. Prasad and M.S. Raghunathan, `Topological central extensions of semi-simple groups over local fields.' Annals of Math. 119 (1984), pp. 133-181. MR 86e:20051a; MR 86e:20051b

[R]
R. R. Rao, `On some explicit formulas in the theory of the Weil representation.' Pacific J. of Math. 157 (1993), pp. 133-181. MR 94a:22037

[Ru1]
K. Rumelhart, Minimal Representations of Exceptional $p$-adic Groups. Harvard University Thesis, 1995.

[Ru2]
K. Rumelhart, `An automorphic theta module for a rank two form of $E_6$.' Preprint.

[S1]
G. Savin, `An analogue of the Weil representation for $G_2$.' J. Reine. und Angew. Math. 434 (1993), pp. 133-181. MR 94a:22038

[S2]
G. Savin, `Dual pair $G_{{\mathcal {J}}} \times \operatorname {PGL}_2$; $G_{{\mathcal {J}}}$ is the automorphism group of the Jordan algebra ${\mathcal {J}}$.' Inventiones Math. 118 (1994), pp. 141-160. MR 95i:22017

[Sch]
R. Schafer, An Introduction to Nonassociative Algebras, Academic Press, 1966. MR 35:1643

[St]
R. Steinberg, Lectures on Chevalley Groups, Lecture Notes, Yale Math. Dept., 1968. MR 57:6215

[T1]
J. Tits, Buildings of Special Type and Finite $BN$-pairs, Lecture Notes in Math. 386, Springer-Verlag, 1974. MR 57:9866

[T2]
J. Tits, `Reductive groups over local fields.' In Automorphic Forms, Representations, and $L$-functions, Proc. of Symp. Pure Math. 33 Part I, 1979, pp. 29-69. MR 80h:20064

[To]
P. Torasso, `Méthod des orbits de Kirillov-Duflo, orbites nilpotentes et représentations associées.' Preprint.

[W]
A. Weil, `Sur certain group d'opérateurs unitaires.' Acta Math. 111 (1964), pp. 133-181. MR 29:2324

Similar Articles:

Retrieve articles in Representation Theory with MSC (1991): 22E35, 22E50, 17B25, 17B60, 11F70, 11F27, 17C50

Retrieve articles in all Journals with MSC (1991): 22E35, 22E50, 17B25, 17B60, 11F70, 11F27, 17C50

Additional Information:

Karl E. Rumelhart
Affiliation: Department of Mathematics, Building 380, Stanford University, Stanford, California 94305-2125
Email: ker@math.stanford.edu

DOI: 10.1090/S1088-4165-97-00009-5
PII: S 1088-4165(97)00009-5
Received by editor(s): October 22, 1996
Received by editor(s) in revised form: April 3, 1997
Posted: June 19, 1997
Copyright of article: Copyright 1997, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google