Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article
     

On inversion of the Bessel and Gelfand transforms

Author(s): Masaaki Furusawa; Joseph A. Shalika
Journal: Trans. Amer. Math. Soc. 354 (2002), 837-852.
MSC (2000): Primary 22E35; Secondary 11F70, 11F72
Posted: July 12, 2001
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

We construct the Plancherel measure corresponding to the Bessel model on the split special orthogonal group of $\text{odd degree}\ge 5$ and the Whittaker model on a connected split reductive group in general. As an application we prove the inversion formula which expresses the related integral transform in terms of the Satake transform.

References:

1.
D. Bump, S. Friedberg and M. Furusawa, Explicit formulas for the Waldspurger and Bessel models, Israel J. Math. 102 (1997), 125-177. MR 98k:22070

2.
W. Casselman, The unramified principal series of $\mathfrak{p}$-adic groups I. The spherical function, Compositio Math. 40 (1980), 387-406. MR 83a:22018

3.
W. Casselman and J. Shalika, The unramified principal series of $p$-adic groups II. The Whittaker function, Compositio Math. 41 (1980), 207-231. MR 83i:22027

4.
M. Furusawa and J. A. Shalika, On central critical values for the degree four $L$-functions for ${\mathrm{GSp}}\left(4\right)$: The fundamental lemma, preprint.

5.
I. G. Macdonald, Spherical functions on a group of $p$-adic type, Publications of the Ramanujan Institute, No. 2. Ramanujan Institute, Center for Advanced Study in Mathematics, University of Madras, Madras, 1971. MR 55:8261

6.
M. Novodvorsky, New unique models of representations of unitary groups, Compositio Math. 33 (1976), 289-295. MR 58:11244

7.
Y. Ye, The fundamental lemma of a relative trace formula for $\mathrm{GL}\left(3\right)$, Compositio Math. 89 (1993), 121-162. MR 95b:22023

8.
Y. Ye, An integral transform and its applications, Math. Ann. 300 (1994), 405-417. MR 95j:11045

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 22E35, 11F70, 11F72

Retrieve articles in all Journals with MSC (2000): 22E35, 11F70, 11F72

Additional Information:

Masaaki Furusawa
Affiliation: Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto 3--3--138, Sumiyoshi-ku, Osaka~558--8585, Japan
Email: furusawa@sci.osaka-cu.ac.jp

Joseph A. Shalika
Affiliation: Department of Mathematics, The Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218
Email: shalika@math.jhu.edu

DOI: 10.1090/S0002-9947-01-02866-5
PII: S 0002-9947(01)02866-5
Received by editor(s): August 7, 2000
Received by editor(s) in revised form: February 26, 2001
Posted: July 12, 2001
Additional Notes: The research of Furusawa was partially supported by the Sumitomo Foundation and the Grant-in-Aid for Scientific Research No.~10640028, the Ministry of Education, Science, Sports and Culture of Japan
Copyright of article: Copyright 2001, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google