Proof of Vogan's conjecture on Arthur packets for $\mathop{GL}_n$ over $p$-adic fields

TL;DR

This paper proves Vogan's conjecture on Arthur packets for general linear groups over p-adic fields, utilizing endoscopic lifting techniques adapted from real group cases, advancing the understanding of representation theory in p-adic contexts.

Contribution

It provides a proof of Vogan's conjecture for GL_n over p-adic fields, extending endoscopic lifting methods from real to p-adic groups.

Findings

Vogan's conjecture for GL_n over p-adic fields is confirmed.

Endoscopic lifting techniques are successfully adapted to p-adic groups.

The proof builds on and extends earlier work by Adams, Barbasch, and Vogan.

Abstract

In this paper we prove Vogan's conjecture on Arthur packets for general linear groups over $p$-adic fields, building on earlier work. The proof uses a special case of endoscopic lifting, adapted from the 1992 book by Adams, Barbasch and Vogan, where it was articulated for real groups.