Some Unipotent Arthur Packets for Reductive p-adic Groups

Abstract

Abstract Let ${\textsf k}$ be a $p$-adic field, and let $\textbf {G}({\textsf k})$ be the ${\textsf k}$-points of a connected reductive group, inner to split. The set of Aubert–Zelevinsky duals of the constituents of a tempered L-packet forms an Arthur packet for $\textbf {G}({\textsf k})$. In this paper, we give an alternative characterization of such Arthur packets in terms of the wavefront set, proving in some instances a conjecture of Jiang–Liu and Shahidi. Pursuing an analogy with real and complex groups, we define some special unions of Arthur packets, which we call weak Arthur packets and describe their constituents in terms of their Langlands parameters.