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

2022/06/02 by Clifton Cunningham, Cunningham, Clifton, Mishty Ray +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2206.01027

openalex publication_date 2022/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 × SL₂(ℂ) × SL₂(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.

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• Proof of the p-adic Kazhdan-Lusztig hypothesis for GL(n)

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