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, as recalled in Cunningham et al. [Arthur packets for p-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples, Memoirs of the American Mathematical Society, Boston, 2022, Section 8.3, Conjecture 1(a)], for irreducible Arthur parameters of p-adic general linear groups. This result shows that these Arthur packets may be characterized by properties of simple perverse sheaves on a moduli space of Langlands parameters.