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On a Conjecture of Jacquet, Lai, and Rallis: Some Exceptional Cases

Published online by Cambridge University Press:  20 November 2018

David Ginzburg  and
Erez Lapid
David Ginzburg
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
Erez Lapid
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Abstract

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We prove two spectral identities. The first one relates the relative trace formula for the spherical variety $\text{GSpin(4,}\,\text{3)/}{{G}_{2}}$ with a weighted trace formula for $G{{L}_{2}}$. The second relates a spherical variety pertaining to ${{F}_{4}}$ to one of $GSp\left( 6 \right)$. These identities are in accordance with a conjecture made by Jacquet, Lai, and Rallis, and are obtained without an appeal to a geometric comparison.

Keywords

11F7011F7211F3011F67
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 6 , 01 December 2007 , pp. 1323 - 1340
Copyright
Copyright © Canadian Mathematical Society 2007

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