${\text{SL}}_3$ dual pairs

We study the exceptional theta correspondence for dual pairs of the form ${\text{SL}}_3\times G$ 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 ${\text{SL}}_3$. Our dual pair is in a see-saw relationship with a dual pair of the form $G_2\times H$ such that $G\mathrm{/}H$ is a rank-two symmetric space. Using the theta correspondence for ${\text{SL}}_3\times G$, we prove a multiplicity-one result for $H$-invariant functionals on representations of $G$.