Vol. 255, No. 2, 2012

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

Moshe Adrian

Vol. 255 (2012), No. 2, 257–280

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 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).

local Langlands correspondence, p-adic groups, Langlands program, representation theory, number theory
Mathematical Subject Classification 2010
Primary: 11S37, 22E50
Received: 10 November 2010
Revised: 15 February 2012
Accepted: 7 March 2012
Published: 10 April 2012
Moshe Adrian
Mathematics Department
University of Utah
155 S 1400 E, Room 233
Salt Lake City, UT 84112-0090
United States