Vogan's Conjecture on local Arthur packets of $p$-adic ${\mathrm{GL}}_n$ and a combinatorial Lemma

Abstract

For ${\mathrm{GL}}_n$ over a $p$-adic field, Cunningham and Ray proved Vogan's conjecture, that is, local Arthur packets are the same as ABV packets. They used the endoscopic theory to reduce the general case to a combinatorial lemma for irreducible local Arthur parameters, and their proof implies that one can also prove Vogan's conjecture for $p$-adic ${\mathrm{GL}}_n$ by proving a generalized version of this combinatorial lemma. Riddlesden recently proved this generalized lemma. In this paper, we give a new proof of it, which has its own interest.

21 pages, comments are welcome

References in corpus (1)

• Appearance of the Kashiwara-Saito singularity in the representation theory of $p$-adic ${\mathrm{GL}}_{16}$