On the local Langlands correspondences of DeBacker–Reeder and Reeder for GL(ℓ,F), where ℓ is prime

Moshe Adrian

Vol. 255 (2012), No. 2, 257–280

DOI: 10.2140/pjm.2012.255.257

Abstract

We prove that the conjectural depth-zero local Langlands correspondence of DeBacker and Reeder agrees with the known depth-zero local Langlands correspondence for the group GL(ℓ,F), where ℓ is prime and F is a nonarchimedean local field of characteristic 0. We also prove that if one assumes a certain compatibility condition between Adler’s and Howe’s constructions of supercuspidal representations, then the conjectural positive-depth local Langlands correspondence of Reeder also agrees with the known positive-depth local Langlands correspondence for GL(ℓ,F).

Keywords

local Langlands correspondence, p-adic groups, Langlands program, representation theory, number theory

Mathematical Subject Classification 2010

Primary: 11S37, 22E50

Milestones

Received: 10 November 2010

Revised: 15 February 2012

Accepted: 7 March 2012

Published: 10 April 2012