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
     

On square-integrable representations of classical $p$-adic groups II

Author(s): Chris Jantzen
Journal: Represent. Theory 4 (2000), 127-180.
MSC (2000): Primary 22E50
Posted: February 23, 2000
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

In this paper, we continue our study of non-supercuspidal discrete series for the classical groups $Sp(2n,F)$, $SO(2n+1,F)$, where $F$ is $p$-adic.

References:

[Aub]
A.-M. Aubert, Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d'un groupe réductif $p$-adique, Trans. Amer. Math. Soc., 347 (1995), 2179-2189, and Erratum à "Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d'un groupe réductif $p$-adique'', Trans. Amer. Math. Soc., 348 (1996), 4687-4690. MR 95i:22025; MR 97c:22019

[BDK]
J. Bernstein, P. Deligne, and D. Kazhdan, Trace Paley-Wiener theorem for reductive $p$-adic groups, J. Analyse Math., 47 (1986), 180-192. MR 88g:22016

[B-Z]
I. Bernstein and A. Zelevinsky, Induced representations of reductive $p$-adic groups $I$, Ann. Sci. École Norm. Sup., 10 (1977), 441-472. MR 58:28310

[B-W]
A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, Princeton University Press, Princeton, 1980. MR 83c:22018

[Cas]
W. Casselman, Introduction to the theory of admissible representations of $p$-adic reductive groups, preprint.

[Gol]
D. Goldberg, Reducibility of induced representations for $Sp(2n)$ and $SO(n)$, Amer. J. Math., 116 (1994), 1101-1151. MR 95g:22016

[Jan1]
C. Jantzen, Reducibility of certain representations for symplectic and odd-orthogonal groups, Comp. Math., 104 (1996), 55-63. MR 98d:22014

[Jan2]
C. Jantzen, On supports of induced representations for symplectic and odd-orthogonal groups, Amer. J. Math., 119 (1997), 1213-1262. MR 99b:22028

[Jan3]
C. Jantzen, Some remarks on degenerate principal series, Pac. J. Math., 186 (1998), 67-87. MR 99j:22018

[Jan4]
C. Jantzen, On square-integrable representations of classical $p$-adic groups, to appear, Can. J. Math.

[M\oe1]
C. M\oeglin, Représentations unipotentes et formes automorphes de carré intégrable, Forum Math., 6 (1994), 651-744. MR 95k:22024

[M\oe2]
C. M\oeglin, Normalisation des opérateurs d'entrelacement et réductibilité des induites des cuspidales; le cas des groupes classiques $p$-adiques, to appear, Ann. of Math.

[M\oe3]
C. M\oeglin, Sur la classification des séries discrètes des groupes classiques; paramatres de Langlands et exhaustivité, preprint.

[Mu]
G. Muic Some results on square integrable representations; Irreducibility of standard representations, IMRN, 14 (1998), 705-726. MR 99f:22031

[M-R]
F. Murnaghan and J. Repka, Reducibility of induced representations of split classical $p$-adic groups, Comp. Math., 114 (1998), 263-313. MR 99m:22021

[Re]
M. Reeder, Hecke algebras and harmonic analysis on $p$-adic groups, Amer. J. Math., 119 (1997), 225-248. MR 99c:22025

[S-S]
P. Schneider and U. Stuhler, Representation theory and sheaves on the Bruhat-Tits building, Publ. Math. IHES, 85 (1997), 97-191. MR 98m:22023

[Sha1]
F. Shahidi, A proof of Langlands conjecture on Plancherel measure; complementary series for $p$-adic groups Ann. of Math., 132 (1990), 273-330. MR 91m:11095

[Sha2]
F. Shahidi, Twisted endoscopy and reducibility of induced representations for $p$-adic groups Duke Math. J., 66 (1992), 1-41. MR 93b:22034

[Sil1]
A. Silberger, The Langlands quotient theorem for $p$-adic groups, Math. Ann., 236 (1978), 95-104. MR 58:22413

[Sil2]
A. Silberger, Special representations of reductive $p$-adic groups are not integrable, Ann. of Math., 111 (1980), 571-587. MR 82k:22015

[Tad1]
M. Tadic, Representations of $p$-adic symplectic groups, Comp. Math., 90 (1994), 123-181. MR 95a:22025

[Tad2]
M. Tadic, Structure arising from induction and Jacquet modules of representations of classical $p$-adic groups, J. of Algebra, 177 (1995), 1-33. MR 97b:22023

[Tad3]
M. Tadic, On reducibility of parabolic induction, Israel J. Math., 107 (1998), 159-210. CMP 99:05

[Tad4]
M. Tadic, On regular square integrable representations of $p$-adic groups, Amer. J. Math., 120 (1998), 159-210. MR 99h:22026

[Tad5]
M. Tadic, On square integrable representations of classical $p$-adic groups, preprint.

[Tad6]
M. Tadic, Square integrable representations of classical $p$-adic groups corresponding to segments, Represent. Theory, 3 (1999), 58-89. CMP 99:15

[Zel]
A. Zelevinsky, Induced representations of reductive $p$-adic groups $II$, On irreducible representations of $GL(n)$, Ann. Sci. École Norm. Sup., 13 (1980), 165-210. MR 83g:22012

[Zh]
Y. Zhang, L-packets and reducibilities, J. Reine Angew. Math., 510 (1999), 83-102. CMP 99:14

Similar Articles:

Retrieve articles in Representation Theory with MSC (2000): 22E50

Retrieve articles in all Journals with MSC (2000): 22E50

Additional Information:

Chris Jantzen
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: jantzen@math.ohio-state.edu

DOI: 10.1090/S1088-4165-00-00081-9
PII: S 1088-4165(00)00081-9
Received by editor(s): July 28, 1999
Received by editor(s) in revised form: October 18, 1999
Posted: February 23, 2000
Copyright of article: Copyright 2000, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google