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

TL;DR

This paper constructs local Arthur packets for a specific class of representations of the split reductive group G_2 over nonarchimedean fields, using an exceptional theta correspondence.

Contribution

It introduces a novel construction of local Arthur packets for dihedral long root A-parameters of G_2 via an exceptional theta correspondence.

Findings

Construction of local Arthur packets for G_2 with dihedral long root A-parameters.

Use of an exceptional correspondence involving PU_3 and G_2.

Provides explicit methods for associating representations to A-parameters.

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 $(\mathrm{PU}_3\rtimes \mathbb{Z}/2\mathbb{Z}, G_2)$.