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On Bessel distributions for quasi-split groups

Author: Ehud Moshe Baruch
Journal: Trans. Amer. Math. Soc. 353 (2001), 2601-2614
MSC (2000): Primary 22E50; Secondary 11F70
Published electronically: March 8, 2001
MathSciNet review: 1828462
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We show that the Bessel distribution attached by Gelfand and Kazhdan and by Shalika to a generic representation of a quasi-split reductive group over a local field is given by a function when it is restricted to the open Bruhat cell. As in the case of the character distribution, this function is real analytic for archimedean fields and locally constant for non-archimidean fields.

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Additional Information

Ehud Moshe Baruch
Affiliation: Theoretical Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Address at time of publication: Department of Mathematics, University of California at Santa Cruz, Santa Cruz, California 95064

Keywords: Bessel distributions, Bessel functions
Received by editor(s): November 14, 1998
Received by editor(s) in revised form: July 7, 1999
Published electronically: March 8, 2001
Article copyright: © Copyright 2001 American Mathematical Society