  Let $G$ be a split simply laced group defined over a $p$-adic field $F$. In
this paper we study the restriction of the minimal representation of $G$ to
various dual pairs in $G$. For example, the restriction of the minimal
representation of $E_7$ to the dual pair $G_2 \times{}$Sp(6) gives the
non-endoscopic Langlands lift of irreducible representations of $G_2$ to Sp(6).
