Dihedral long root A-packets of $p$-adic $G_2$ via theta correspondence

Abstract

We construct local Arthur packets associated with a dihedral long root $A$-parameter of a split reductive group of type $G_2$ over a nonarchimedian local field of characteristic zero. The construction relies on an exceptional correspondence for the pair $({\mathrm{PU}}_3⋊\mathbb{Z}/2\mathbb{Z},G_2)$.

41 pages. Comments welcome