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