Speakers:  Omer Offen (Brandeis University)

Title:  A new application of the residue method 

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) × 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.