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Jacquet modules of the Weil representations and families of relative trace identities

Published online by Cambridge University Press:  04 December 2007

Zhengyu Mao
Affiliation:
Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, NJ 07102, USAzmao@andromeda.rutgers.edu
Stephen Rallis
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USAhaar@math.ohio-state.edu
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Abstract

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In this paper we show how to predict relative trace identities from the computation of Jacquet modules of the Weil representations. Many previously considered special cases of relative trace identities fit the principle we develop here, including those with important applications on L-functions. We also show how to prove these identities using the Weil representation. We give a proof of the relative trace identities between the distributions on SO(n + 1, n) and $\widetilde{\textit{Sp}}(m)$$(n\geq m)$. The proof should serve as a model to the other cases conjectured in the paper.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2004
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