On the asymptotics of Whittaker functions
Authors:
Erez Lapid and Zhengyu Mao
Journal:
Represent. Theory 13 (2009), 63-81
MSC (2000):
Primary 22E50, 11F70
DOI:
https://doi.org/10.1090/S1088-4165-09-00343-4
Published electronically:
April 2, 2009
Erratum:
Represent. Theory 13 (2009), 348-348.
MathSciNet review:
2495561
Full-text PDF Free Access
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.
- I. N. Bernšteĭn and A. V. Zelevinskiĭ, Representations of the group $GL(n,F),$ where $F$ is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5–70 (Russian). MR 0425030
- J. W. Cogdell and I. I. Piatetski-Shapiro, Derivatives and ${L}$-functions for ${G}{L}(n)$, To appear.
- W. Casselman and J. Shalika, The unramified principal series of $p$-adic groups. II. The Whittaker function, Compositio Math. 41 (1980), no. 2, 207–231. MR 581582
- I. M. Gel′fand and D. A. Kajdan, Representations of the group ${\rm GL}(n,K)$ where $K$ 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
- Roger Godement, Notes on Jacquet-Langlands’ theory, (mimeographed notes).
- Hervé Jacquet, Ilja Iosifovitch Piatetski-Shapiro, and Joseph Shalika, Automorphic forms on ${\rm GL}(3)$. I, Ann. of Math. (2) 109 (1979), no. 1, 169–212. MR 519356, DOI https://doi.org/10.2307/1971270
- H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika, Conducteur des représentations du groupe linéaire, Math. Ann. 256 (1981), no. 2, 199–214 (French). MR 620708, DOI https://doi.org/10.1007/BF01450798
- Hervé Jacquet and Joseph Shalika, Exterior square $L$-functions, Automorphic forms, Shimura varieties, and $L$-functions, Vol. II (Ann Arbor, MI, 1988) Perspect. Math., vol. 11, Academic Press, Boston, MA, 1990, pp. 143–226. MR 1044830
- Hervé Jacquet and Joseph Shalika, 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
- François Rodier, Whittaker models for admissible representations of reductive $p$-adic split groups, Harmonic analysis on homogeneous spaces (Proc. Sympos. Pure Math., Vol. XXVI, Williams Coll., Williamstown, Mass., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 425–430. MR 0354942
- J. A. Shalika, The multiplicity one theorem for ${\rm GL}_{n}$, Ann. of Math. (2) 100 (1974), 171–193. MR 348047, DOI https://doi.org/10.2307/1971071
- Dani Szpruch, Uniqueness of Whittaker model for the metaplectic group, Pacific J. Math. 232 (2007), no. 2, 453–469. MR 2366363, DOI https://doi.org/10.2140/pjm.2007.232.453
- Nolan R. Wallach, Real reductive groups. II, Pure and Applied Mathematics, vol. 132, Academic Press, Inc., Boston, MA, 1992. MR 1170566
Retrieve articles in Representation Theory of the American Mathematical Society 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
MR Author ID:
631395
Email:
erezla@math.huji.ac.il
Zhengyu Mao
Affiliation:
Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102
MR Author ID:
326784
Email:
zmao@rutgers.edu
Received by editor(s):
July 23, 2008
Received by editor(s) in revised form:
December 1, 2008
Published electronically:
April 2, 2009
Additional Notes:
This research partially funded by grant #2004200 from the United States-Israel Binational Science Foundation
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
