Howe duality for a quasi-split exceptional dual pair

Abstract

We prove Howe duality for the theta correspondence arising from the $p$-adic dual pair $G_2\times ({\text{PU}}_3⋊\mathbb{Z}/2\mathbb{Z})$ inside the adjoint quasi-split group of type $E_6$.

arXiv commentv3: added sections 5 and 6; minor corrections