Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Self-contragredient supercuspidal representations of $ \mathrm {GL}_n$

Author(s): Jeffrey D. Adler
Journal: Proc. Amer. Math. Soc. 125 (1997), 2471-2479.
MSC (1991): Primary 22E50; Secondary 20G05, 11F70
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Let $F$ be a non-archimedean local field of residual characteristic $p$. Then $\mathrm {GL}_n(F)$ has tamely ramified self-contragredient supercuspidal representations if and only if $n$ or $p$ is even. When such representations exist, they do so in abundance.

References:

1.
C. J. Bushnell and P. Kutzko, The admissible dual of $\hbox {GL}_{N}$ via restriction to compact open subgroups, Ann. of Math. Studies, vol. 129, Princeton University Press, 1993. MR 94h:22007

2.
I. M. Gelfand and M. I. Graev, The group of matrices of second order with coefficients in a locally compact field and special functions on locally compact fields, Uspekhi Mat. Nauk 18 (1963), 29-99. MR 27:5864

3.
I. M. Gelfand and D. A. Kazhdan, Representations of $ \mathrm {GL}(n,{K})$ where ${K}$ is a local field, Lie groups and their representations: Proc. Summer School on representation theory, Hungary, 1971 (I. M. Gelfand, ed.), 1975, pp. 95-118. MR 53:8334

4.
R. Howe, Tamely ramified supercuspidal representations of $\hbox {GL}_n$, Pac. J. Math. 73 (1977), no. 2, 437-460. MR 58:11241

5.
G. Lusztig, Characters of reductive groups over a finite field, Ann. of Math. Studies, vol. 107, Princeton University Press, 1984. MR 86j:20038

6.
L. Morris, Level zero ${G}$-types, preprint.

7.
A. Moy, Local constants and the tame Langlands correspondence, Amer. J. Math. 108 (1986), 863-930. MR 88b:11081

8.
A. Moy and G. Prasad, Unrefined minimal ${K}$-types for $p$-adic groups, Inv. Math. 116 (1994), 393-408. MR 95f:22023

9.
-, Jacquet functors and unrefined minimal ${K}$-types, Comm. Math. Helv., to appear. CMP 96:07

10.
P. J. Sally, Jr., Invariant subspaces and Fourier-Bessel transforms on the $\mathfrak {p}$-adic plane, Math. Ann. 174 (1967), 247-264. MR 58:28317

11.
J.-P. Serre, Corps locaux, Hermann, 1962. MR 27:133

12.
F. Shahidi, Twisted endoscopy and reducibility of induced representations for $p$-adic groups, Duke Math. J., 66 (1992), 1-41. MR 93b:22034

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 22E50, 20G05, 11F70

Retrieve articles in all Journals with MSC (1991): 22E50, 20G05, 11F70

Additional Information:

Jeffrey D. Adler
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: jeff@math.uchicago.edu

DOI: 10.1090/S0002-9939-97-03786-6
PII: S 0002-9939(97)03786-6
Received by editor(s): December 1, 1995
Received by editor(s) in revised form: February 12, 1996
Communicated by: Roe W. Goodman
Copyright of article: Copyright 1997, American Mathematical Society

Forward Citation(s):

Information for authors on submitting citations

The following works have cited this article

Fiona Murnaghan and Joe Repka, Reducibility of induced representations of split classical $p$-adic groups, Comp. Math. (3) 114 (1998), 263-313. MR 99m:22021

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

Fiona Murnaghan and Joe Repka, Reducibility of some induced representations of $p$-adic unitary groups,Trans. Amer. Math. Soc. 351(1999),   193-210.

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