A new application of the residue method

Abstract: The relative Langlands program studies the relations between functorial transfers of automorphic representations from one group $G'$ to another group $G$, period integrals over a subgroup $H$ of $G$ and special $L$-values. When $(G,H)$ is a vanishing pair, that is, every cusp form of G has a vanishing $H$-period, it is of interest to study discrete automorphic representations that admit a non-vanishing $H$-period. For this task, Jacquet and Rallis developed the residue method. It has since been used extensively, mostly for representations with cuspidal data lying in a maximal Levi subgroup of G. In this talk we focus on the case where $H=Sp(a)\times Sp(b)$ lies in $G=Sp(a+b)$. We will introduce a new construction of some residual representations of G that admit H-periods. This is joint work in progress with Sol Friedberg and David Ginzburg.

number theoryrepresentation theory

Audience: researchers in the topic

MIT number theory seminar

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