Generalization of a Theorem of Waldspurger to Nice Representations
Identifieur interne : 000F77 ( Main/Exploration ); précédent : 000F76; suivant : 000F78Generalization of a Theorem of Waldspurger to Nice Representations
Auteurs : D. Kazhdan [États-Unis] ; A. Polishchuk [États-Unis]Source :
- Progress in Mathematics ; 2003.
Abstract
Abstract: This paper presents some examples of equalities of integrals over local fields of characteristic zero predicted by the stationary phase approximation. These examples should be considered in the context of algebraic integration theory, proposed by the first author in [6]. From the point of view of this theory, our main theorem gives examples of pairs of algebro-geometric data over a given local field E producing equal integrals over arbitrary finite extensions of E. Another motivation for this work is the theory of Sato’s functional equations associated with prehomogeneous vector spaces over local fields. As an application of our techniques, we find an explicit form of these equations for the action of GLnon symmetric n x n matrices in the case when n is odd (this is a generalization of a particular case of the equations obtained by W. J. Sweet Jr. in [24]).
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DOI: 10.1007/978-1-4612-0029-1_10
Affiliations:
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