Proof of Vogan's conjecture on Arthur packets: irreducible parameters of p-adic general linear groups

TL;DR

This paper proves Vogan's conjecture for a specific class of irreducible Arthur parameters in p-adic general linear groups, linking Arthur packets to properties of perverse sheaves on moduli spaces.

Contribution

It establishes the characterization of Arthur packets for irreducible parameters via simple perverse sheaves, confirming a key conjecture in the local Langlands program.

Findings

Vogan's conjecture is proven for irreducible Arthur parameters.

Arthur packets are characterized by properties of perverse sheaves.

The result advances understanding of the local Langlands correspondence for p-adic groups.

Abstract

In this paper we prove Vogan's conjecture on local Arthur packets, for Arthur parameters of $p$-adic general linear groups that are irreducible as representations of $W_F \times SL_2(\mathbb{C}) \times SL_2(\mathbb{C})$ - we refer to such parameters as irreducible Arthur parameters. This result shows that these Arthur packets may be characterized by properties of simple perverse sheaves on a moduli space of Langlands parameters.