Exceptional Dual Pair Correspondences and Functoriality

I will discuss certain dual pairs G x G’ occurring in the exceptional groups E_8, E_7, E_6, (and D_5) over a p-adic field. By restricting the minimal representation of the larger group to the dual pair, one obtains a so-called theta correspondence between the representations of G and G’. The use of Jacquet functors gives a way of building up an inductive” process to prove that, for spherical representations, the theta correspondence is functorial. This is joint work with Gordan Savin.