Arithmetic Study Group: Cusp forms on GSp(4) with non-zero SO(4) periods
26 May 2011 16:15 in CM219
Abstract: I will briefly explain the ideas behind the relative trace formula and outline a specific case of application. Namely: the Saito-Kurokawa lifting of automorphic representations from PGL(2) to the projective symplectic group of similitudes PGSp(4) of genus 2 established by the use of the relative trace formula, thus characterising the image as the representations with a nonzero period for the special orthogonal group SO(4,E/F) associated to a quadratic extension E of the base field F, and a nonzero Fourier coefficient for a generic character of the unipotent radical of the Siegel parabolic subgroup. The image is nongeneric and almost everywhere nontempered, violating a naive generalization of the Ramanujan conjecture.