Some Unipotent Arthur Packets for Reductive $p$-adic Groups

TL;DR

This paper provides a new characterization of certain Arthur packets for reductive p-adic groups using wavefront sets, confirming some conjectures and defining special unions called weak Arthur packets.

Contribution

It offers an alternative description of Arthur packets via wavefront sets and introduces weak Arthur packets based on Langlands parameters, extending understanding of p-adic group representations.

Findings

Characterization of Arthur packets using wavefront sets

Confirmation of Jiang-Liu and Shahidi conjectures in some cases

Definition of weak Arthur packets and their constituents

Abstract

Let $k$ be a $p$-adic field and let $\mathbf{G}(k)$ be the $k$-points of a connected reductive group, inner to split. The set of Aubert-Zelevinsky duals of the constituents of a tempered L-packet form an Arthur packet for $\mathbf{G}(k)$. 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 \emph{weak} Arthur packets and describe their constituents in terms of their Langlands parameters.