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On the asymptotics of Whittaker functions

Authors: Erez Lapid and Zhengyu Mao
Journal: Represent. Theory 13 (2009), 63-81
MSC (2000): Primary 22E50, 11F70
Published electronically: April 2, 2009
Erratum: Represent. Theory 13 (2009), 348.
MathSciNet review: 2495561
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Abstract: We study the asymptotics of Whittaker functions on split groups and relate them to the cuspidal exponents of the representation.

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  • [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. MR 0425030 (54:12988)
  • [CPS] J. W. Cogdell and I. I. Piatetski-Shapiro, Derivatives and $ {L}$-functions for $ {G}{L}(n)$, To appear.
  • [CS80] W. Casselman and J. Shalika, The unramified principal series of $ p$-adic groups. II. The Whittaker function, Compositio Math. 41 (1980), no. 2, 207-231. MR 581582 (83i:22027)
  • [GK75] I. M. Gel$ '$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 (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 $ {\rm GL}(3)$. 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 $ 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 (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 $ p$-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 $ {\rm GL}_{n}$, 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)

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Additional Information

Erez Lapid
Affiliation: Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem Israel, 91904

Zhengyu Mao
Affiliation: Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102

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.

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