Type: Article
Publication Date: 1992-06-01
Citations: 37
DOI: https://doi.org/10.2140/pjm.1992.154.265
If G is a reductive group quasi-split over a number field F and K the kernel of the trace formula, one can integrate K in the two variables against a generic character of a maximal unipotent subgroup N to obtain the Kuznietsov trace formula.If H is the fixator of an involution of G, one can also integrate K in one variable over H and in the other variable against a generic character of N: one obtains then a "relative" version of the Kuznietsov trace formula.We propose as a conjecture that the relative Kuznietsov trace formula can be "matched" with the Kuznietsov trace formula for another group G'.A consequence of this formula would be the characterization of the automorphic representations of G which admit an element whose integral over H is non-zero: they should be functorial image of representations of G'.In this article, we study the case where H is the symplectic group inside the linear group; we prove the "fundamental lemma" for the situation at hand and outline the identity of the trace formulas.This case is elementary and should serve as a model for the general case.