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.
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.
- [BZ76] 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
- [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 𝑝-adic groups. II. The Whittaker function, Compositio Math. 41 (1980), no. 2, 207–231. MR 581582
- [GK75] I. M. Gel′fand and D. A. Kajdan, Representations of the group 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
- [God70] Roger Godement, Notes on Jacquet-Langlands' theory, (mimeographed notes).
- [JPSS79] Hervé Jacquet, Ilja Iosifovitch Piatetski-Shapiro, and Joseph Shalika, Automorphic forms on 𝐺𝐿(3). I, Ann. of Math. (2) 109 (1979), no. 1, 169–212. MR 519356, https://doi.org/10.2307/1971270
- [JPSS81] 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, https://doi.org/10.1007/BF01450798
- [JS90a] 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
- [JS90b] 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
- [Rod73] 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
- [Sha74] J. A. Shalika, The multiplicity one theorem for 𝐺𝐿_{𝑛}, Ann. of Math. (2) 100 (1974), 171–193. MR 348047, https://doi.org/10.2307/1971071
- [Szp07] Dani Szpruch, Uniqueness of Whittaker model for the metaplectic group, Pacific J. Math. 232 (2007), no. 2, 453–469. MR 2366363, https://doi.org/10.2140/pjm.2007.232.453
- [Wal92] Nolan R. Wallach, Real reductive groups. II, Pure and Applied Mathematics, vol. 132, Academic Press, Inc., Boston, MA, 1992. MR 1170566
where 
is a local non-Archimedean field, Uspehi Mat. Nauk 31 (1976), no. 3(189), 5-70. 
-adic groups. II. The Whittaker function, Compositio Math. 41 (1980), no. 2, 207-231. 
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. 
. I, Ann. of Math. (2) 109 (1979), no. 1, 169-212. 
-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. 
-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. 
, Ann. of Math. (2) 100 (1974), 171-193. Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 22E50, 11F70
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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:
https://doi.org/10.1090/S1088-4165-09-00343-4
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.
