Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165

Journals Home Search My Subscriptions Subscribe
Previous volume | This volume | Most recent volume | All volumes | Next volume | Previous article | Next article
Request Permissions
 
 

 

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


Author: Chris Jantzen
Journal: Represent. Theory 4 (2000), 127-180
MSC (2000): Primary 22E50
DOI: https://doi.org/10.1090/S1088-4165-00-00081-9
Published electronically: February 23, 2000
MathSciNet review: 1789464
Full-text PDF Free Access

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

  • [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 of the American Mathematical Society 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: https://doi.org/10.1090/S1088-4165-00-00081-9
Received by editor(s): July 28, 1999
Received by editor(s) in revised form: October 18, 1999
Published electronically: February 23, 2000
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society