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 ${\mathrm{PGL}}_2$.

arXiv comment35 pages, comments are welcome!