|
The Burger-Sarnak method and operations on the unitary dual of
Author(s):
Akshay
Venkatesh
Journal:
Represent. Theory
9
(2005),
268-286.
MSC (2000):
Primary 22E50;
Secondary 11F70
Posted:
March 31, 2005
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study the effect of restriction to Levi subgroups, induction from Levi subgroups, and tensor product, on unitary representations of over a local field . These results give partial answers to questions raised by Clozel.
References:
-
- 1.
-
I. N. Bernstein.
All reductive -adic groups are of type I.
Funkcional. Anal. i Prilozen.,
8(2):3-6, 1974.
MR
0348045 (50 #543)
- 2.
-
M. Burger, J.-S. Li, and P. Sarnak.
Ramanujan duals and automorphic spectrum.
Bull. Amer. Math. Soc. (N.S.),
26(2):253-257, 1992.
MR
1118700 (92h:22023)
- 3.
-
L. Clozel.
Spectral theory of automorphic forms.
Preprint.
- 4.
-
L. Clozel.
Combinatorial consequences of Arthur's
conjectures and the
Burger-Sarnak method.
Int. Math. Res. Not.
2004(11):511-523.
MR
2038775
- 5.
-
L. Clozel and E. Ullmo.
Équidistribution des points
de Hecke.
Contributions to automorphic
forms, geometry, and number
theory, 193-254, Johns Hopkins Univ.
Press, Baltimore, MD, 2004.
MR
2058609
- 6.
-
M. Cowling, U. Haagerup, and R. Howe.
Almost
matrix coefficients.
J. Reine Angew. Math.,
387:97-110, 1988.
MR
0946351 (89i:22008)
- 7.
-
Jacques Dixmier.
-algebras.
North-Holland Publishing Co., Amsterdam,
1977.
Translated from the French by Francis
Jellett, North-Holland
Mathematical Library, Vol. 15.
MR
1393197 (97c:17010)
- 8.
-
J. M. G. Fell.
Weak containment and induced representations
of groups.
Canad. J. Math.,
14:237-268, 1962.
MR
0150241 (27 #242)
- 9.
-
Anthony W. Knapp.
Representation theory of semisimple
groups.
Princeton Landmarks in Mathematics.
Princeton University Press,
Princeton, NJ, 2001.
An overview based on examples, Reprint
of the 1986 original.
MR
1880691 (2002k:22011)
- 10.
-
Robert P. Langlands.
On the functional equations
satisfied by Eisenstein series.
Springer-Verlag, Berlin, 1976.
Lecture Notes in Mathematics, Vol. 544.
MR
0579181 (58 #28319)
- 11.
-
Wenzhi Luo, Zeév Rudnick, and Peter Sarnak.
On the generalized Ramanujan conjecture
for
.
In Automorphic forms, automorphic
representations, and
arithmetic (Fort Worth, TX, 1996),
volume 66 of Proc. Sympos. Pure
Math., pages 301-310. Amer. Math.
Soc., Providence, RI, 1999.
MR
1703764 (2000e:11072)
- 12.
-
George W. Mackey.
The theory of unitary group
representations.
University of Chicago Press, Chicago,
Ill., 1976.
Based on notes by James M. G. Fell and
David B. Lowdenslager of
lectures given at the University of Chicago,
Chicago, Ill., 1955, Chicago
Lectures in Mathematics.
MR
0396826 (53 #686)
- 13.
-
C. Moeglin and J.-L. Waldspurger.
Le spectre résiduel de
.
Ann. Sci. École Norm.
Sup. (4), 22(4):605-674, 1989.
MR
1026752 (91b:22028)
- 14.
-
C. Moeglin and J.-L. Waldspurger.
Spectral decomposition and
Eisenstein series, volume 113 of
Cambridge Tracts in Mathematics.
Cambridge University Press, Cambridge,
1995.
Une paraphrase de l'Écriture
[A paraphrase of Scripture].
MR
1361168 (97d:11083)
- 15.
-
W. Mueller and B. Speh.
On the absolute convergence of the spectral
side of the Arthur trace
formula for
.
arxiv: math.RT/0211030.
- 16.
-
Hee Oh.
Uniform pointwise bounds for matrix
coefficients of unitary
representations and applications to Kazhdan
constants.
Duke Math. J.,
113(1):133-192, 2002.
MR
1905394 (2003d:22015)
- 17.
-
Yehuda Shalom.
Explicit Kazhdan constants for representations
of semisimple and
arithmetic groups.
Ann. Inst. Fourier (Grenoble),
50(3):833-863, 2000.
MR
1779896 (2001i:22019)
- 18.
-
Marko Tadic.
Classification of unitary representations
in irreducible
representations of general linear group (non-Archimedean
case).
Ann. Sci. École Norm.
Sup. (4), 19(3):335-382, 1986.
MR
0870688 (88b:22021)
- 19.
-
Marko Tadic.
Topology of unitary dual of non-Archimedean
.
Duke Math. J.,
55(2):385-422, 1987.
MR
0894588 (89c:22029)
- 20.
-
David Vogan.
Isolated unitary representations.
To appear.
- 21.
-
David A. Vogan, Jr.
The unitary dual of
over an Archimedean field.
Invent. Math.,
83(3):449-505, 1986.
MR
0827363 (87i:22042)
- 22.
-
S. P. Wang.
The dual space of semi-simple Lie groups.
Amer. J. Math.,
91:921-937, 1969.
MR
0259023 (41 #3665)
Similar Articles:
Retrieve articles in Representation Theory
with MSC
(2000):
22E50,
11F70
Retrieve articles in all Journals with MSC
(2000):
22E50,
11F70
Additional Information:
Akshay
Venkatesh
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
Address at time of publication:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012
Email:
akshayv@math.mit.edu
DOI:
10.1090/S1088-4165-05-00226-8
PII:
S 1088-4165(05)00226-8
Received by editor(s):
December 19, 2003
Received by editor(s) in revised form:
January 30, 2005
Posted:
March 31, 2005
Additional Notes:
The author was supported in part by NSF Grant DMS-0245606
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|