Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On inversion of the Bessel and Gelfand transforms
HTML articles powered by AMS MathViewer

by Masaaki Furusawa and Joseph A. Shalika PDF
Trans. Amer. Math. Soc. 354 (2002), 837-852 Request permission

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
  • Daniel Bump, Solomon Friedberg, and Masaaki Furusawa, Explicit formulas for the Waldspurger and Bessel models, Israel J. Math. 102 (1997), 125–177. MR 1489103, DOI 10.1007/BF02773797
  • W. Casselman, The unramified principal series of ${\mathfrak {p}}$-adic groups. I. The spherical function, Compositio Math. 40 (1980), no.Β 3, 387–406. MR 571057
  • W. Casselman and J. Shalika, The unramified principal series of $p$-adic groups. II. The Whittaker function, Compositio Math. 41 (1980), no.Β 2, 207–231. MR 581582
  • 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.
  • I. G. Macdonald, Spherical functions on a group of $p$-adic type, Publications of the Ramanujan Institute, No. 2, University of Madras, Centre for Advanced Study in Mathematics, Ramanujan Institute, Madras, 1971. MR 0435301
  • Mark E. Novodvorsky, New unique models of representations of unitary groups, Compositio Math. 33 (1976), no.Β 3, 289–295. MR 492090
  • Yangbo Ye, The fundamental lemma of a relative trace formula for $\textrm {GL}(3)$, Compositio Math. 89 (1993), no.Β 2, 121–162. MR 1255692
  • Yangbo Ye, An integral transform and its applications, Math. Ann. 300 (1994), no.Β 3, 405–417. MR 1304430, DOI 10.1007/BF01450494
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, OsakaΒ 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
  • Received by editor(s): August 7, 2000
  • Received by editor(s) in revised form: February 26, 2001
  • Published electronically: 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.Β 10640028, the Ministry of Education, Science, Sports and Culture of Japan
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 837-852
  • MSC (2000): Primary 22E35; Secondary 11F70, 11F72
  • DOI: https://doi.org/10.1090/S0002-9947-01-02866-5
  • MathSciNet review: 1862570