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

Abstract

In this paper we prove Vogan's conjecture on local Arthur packets, as recalled in [CFM + 22, Section 8.3, Conjecture 1(a)], for Arthur parameters of p-adic general linear groups that are irreducible and trivial on the Weil group -we refer to such parameters as simple 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.