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

Clifton Cunningham; Mishty Ray

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

Representation Theory 2022-10-11 v2 Number Theory

Authors: Clifton Cunningham , Mishty Ray

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.

Keywords

vogan conjecture arthur packets p-adic general linear groups irreducible arthur parameters langlands parameters perverse sheaves

Cite

@article{arxiv.2206.01027,
  title  = {Proof of Vogan's conjecture on Arthur packets: irreducible parameters of p-adic general linear groups},
  author = {Clifton Cunningham and Mishty Ray},
  journal= {arXiv preprint arXiv:2206.01027},
  year   = {2022}
}

Comments

Main result generalized from from simple parameters to irreducible parameters; allowing ramification

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

Abstract

Keywords

Cite

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