Arthur packets for $\mathrm{G}_2$ over $p$-adic fields

Abstract

We describe Arthur packets for the split reductive group $\mathrm{G}_2$ over a $p$-adic field and compute their stable and endoscopic character distributions. The construction uses the twisted Aubert duality recently studied by Cheng--Kaletha. We identify the corresponding Xu packets on $\mathrm{PGSO}_8$ and their triality-twisted characters. We also extend the result to long-root and short-root Arthur packets corresponding to unitary generic representations of $\mathrm{PGL}_2$.