On the upper bound of wavefront sets of representations of p-adic groups

TL;DR

This paper investigates the upper bounds of wavefront sets for irreducible admissible representations of p-adic groups, proposing a new conjecture and establishing equivalences with existing conjectures in the field.

Contribution

It introduces a new conjecture on wavefront set bounds, reduces it to anti-discrete series representations, and links it to Jiang and ABV packet conjectures.

Findings

Proposes a new conjecture on wavefront set bounds.

Shows the conjecture reduces to anti-discrete series representations.

Establishes equivalence with Jiang and ABV packet conjectures.

Abstract

In this paper we study the upper bound of wavefront sets of irreducible admissible representations of connected reductive groups defined over non-Archimedean local fields of characteristic zero. We formulate a new conjecture on the upper bound and show that it can be reduced to that of anti-discrete series representations, namely, those whose Aubert-Zelevinsky duals are discrete series. Then, we show that this conjecture is equivalent to the Jiang conjecture on the upper bound of wavefront sets of representations in local Arthur packets and also equivalent to an analogous conjecture on the upper bound of wavefront sets of representations in local ABV packets.