  We prove that the conjectural depth zero local Langlands correspondence of
DeBacker/Reeder agrees with the depth zero local Langlands correspondence as
described by Moy, for the group $GL(\ell,F)$, where $\ell$ is prime and F is a
local non-archimedean field of characteristic 0. We also prove that if one
assumes a certain compatibility condition between Adler's and Howe's
construction of supercuspidal representations, then the conjectural positive
depth local Langlands correspondence of Reeder also agrees with the positive
depth local Langlands correspondence as described by Moy, for $GL(\ell,F)$.
Specifically, we first work out in detail the construction of DeBacker/Reeder
for $GL(\ell,F)$, we then restate the constructions in the language of Moy, and
finally prove that the correspondences agree. Up to a compatibility between
Adler's and Howe's constructions, we then do the same for Reeder's positive
depth construction.
