On the weak local Arthur packets conjecture for split classical groups

TL;DR

This paper proves the conjecture that weak local Arthur packets are unions of local Arthur packets for split classical groups over non-Archimedean fields with large residue characteristic, implying unitarity of certain unipotent representations.

Contribution

It establishes the weak local Arthur packets conjecture for split classical groups under specific conditions, advancing understanding of their structure and unitarity.

Findings

Proof of the weak local Arthur packets conjecture for split classical groups

Demonstration of unitarity of unipotent representations in this context

Discussion on generalizations beyond unipotent representations

Abstract

Recently, motivated by the theory of real local Arthur packets, making use of the wavefront sets of representations over non-Archimedean local fields $F$, Ciubotaru, Mason-Brown, and Okada defined the weak local Arthur packets consisting of certain unipotent representations and conjectured that they are unions of local Arthur packets. In this paper, we prove this conjecture for split classical groups with the assumption of the residue field characteristic of $F$ being large. In particular, this implies the unitarity of these unipotent representations. We also discuss the generalization of the weak local Arthur packets beyond unipotent representations which reveals the implications of a conjecture of Jiang on the structure of wavefront sets for representations in local Arthur packets.