\SL_3 dual pairs

Abstract

We study the exceptional theta correspondence for dual pairs of the form \SL_3\times G inside $p$-adic groups of type $E_n$, $n=6,7,8$. We establish Howe duality for lifts of all Whittaker-generic unitarizable representations of \SL_3. Our dual pair is in a see-saw relationship with a dual pair of the form $G_2 \times H$ such that $G/H$ is a rank-two symmetric space. Using the theta correspondence for \SL_3 \times G, we prove a multiplicity-one result for $H$-invariant functionals on representations of $G$.