|
On the asymptotics of Whittaker functions
Author(s):
Erez
Lapid;
Zhengyu
Mao
Journal:
Represent. Theory
13
(2009),
63-81.
MSC (2000):
Primary 22E50, 11F70
Posted:
April 2, 2009
Errata:
Represent. Theory 13 (2009), 348.
MathSciNet review:
2495561
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We study the asymptotics of Whittaker functions on split groups and relate them to the cuspidal exponents of the representation.
References:
-
- [BZ76]
- I. N. Bernšteĭn and A. V. Zelevinskiĭ, Representations of the group
 where  is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5-70. MR 0425030 (54:12988) - [CPS]
- J. W. Cogdell and I. I. Piatetski-Shapiro, Derivatives and
 -functions for  , To appear. - [CS80]
- W. Casselman and J. Shalika, The unramified principal series of
 -adic groups. II. The Whittaker function, Compositio Math. 41 (1980), no. 2, 207-231. MR 581582 (83i:22027) - [GK75]
- I. M. Gel
 fand and D. A. Kajdan, Representations of the group  where  is a local field, Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), Halsted, New York, 1975, pp. 95-118. MR 0404534 (53:8334) - [God70]
- Roger Godement, Notes on Jacquet-Langlands' theory, (mimeographed notes).
- [JPSS79]
- Hervé Jacquet, Ilja Iosifovitch Piatetski-Shapiro, and Joseph Shalika, Automorphic forms on
 . I, Ann. of Math. (2) 109 (1979), no. 1, 169-212. MR 519356 (80i:10034a) - [JPSS81]
- H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, Conducteur des représentations du groupe linéaire, Math. Ann. 256 (1981), no. 2, 199-214. MR 620708 (83c:22025)
- [JS90a]
- Hervé Jacquet and Joseph Shalika, Exterior square
 -functions, Automorphic forms, Shimura varieties, and  -functions, Vol. II (Ann Arbor, MI, 1988), Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990, pp. 143-226. MR 1044830 (91g:11050) - [JS90b]
- -, Rankin-Selberg convolutions: Archimedean theory, Festschrift in honor of I. I. Piatetski-Shapiro on the occasion of his sixtieth birthday, Part I (Ramat Aviv, 1989), Israel Math. Conf. Proc., vol. 2, Weizmann, Jerusalem, 1990, pp. 125-207. MR 1159102 (93d:22022)
- [Rod73]
- François Rodier, Whittaker models for admissible representations of reductive
 -adic split groups, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams College, Williamstown, MA, 1972), Amer. Math. Soc., Providence, RI, 1973, pp. 425-430. MR 0354942 (50:7419) - [Sha74]
- J. A. Shalika, The multiplicity one theorem for
 , Ann. of Math. (2) 100 (1974), 171-193. MR 0348047 (50:545) - [Szp07]
- Dani Szpruch, Uniqueness of Whittaker model for the metaplectic group, Pacific J. Math. 232 (2007), no. 2, 453-469. MR 2366363
- [Wal92]
- Nolan R. Wallach, Real reductive groups. II, Pure and Applied Mathematics, vol. 132, Academic Press Inc., Boston, MA, 1992. MR 1170566 (93m:22018)
Similar Articles:
Retrieve articles in Representation Theory
with MSC
(2000):
22E50, 11F70
Retrieve articles in all Journals with MSC
(2000):
22E50, 11F70
Additional Information:
Erez
Lapid
Affiliation:
Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem Israel, 91904
Email:
erezla@math.huji.ac.il
Zhengyu
Mao
Affiliation:
Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102
Email:
zmao@rutgers.edu
DOI:
10.1090/S1088-4165-09-00343-4
PII:
S 1088-4165(09)00343-4
Received by editor(s):
July 23, 2008
Received by editor(s) in revised form:
December 1, 2008
Posted:
April 2, 2009
Additional Notes:
This research partially funded by grant #2004200 from the United States-Israel Binational Science Foundation
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
