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Moshe Adrian

Publications and source records attributed to Moshe Adrian.

23 records · Page 2Linked to original sources
arXiv2012

On the Local Langlands Correspondences of DeBacker/Reeder and Reeder for $GL(\ell,F)$, where $\ell$ is prime

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.

math.RT↗
arXiv2012

On Hecke algebras and simple supercuspidal representations for Sp(4,F)

A well known result of Borel says that the category of modules over the Iwahori-Hecke algebra of a semisimple p-adic group G describes the Bernstein component associated to the unramified principal series of G. We consider Bernstein components for Sp(4,F) associated to principal series induced from simple supercuspidal representations.

math.RT↗
arXiv2012

A new realization of the Langlands correspondence for PGL(2,F)

In this paper, we give a new realization of the local Langlands correspondence for PGL(2,F), where F is a p-adic field of odd residual characteristic. In this case, supercuspidal representations of PGL(2,F) are parameterized by characters of elliptic tori. Taking a cue from real groups, we propose that supercuspidal representations are naturally parameterized by characters of covers of tori. Over the reals, Harish-Chandra defined the discrete series representations by specifying their characters restricted to an elliptic torus, and these characters may naturally be expressed in terms of characters of a cover of the torus. We write down a natural analogue of Harish-Chandra's character for PGL(2,F), and show that it is the character of a unique supercuspidal representation, on a canonical subset of the elliptic torus. This paves the way for a realization of the local Langlands correspondence for PGL(2,F) that eliminates the need for any character twists.

math.NT↗
arXiv2010

A New Construction for the Tame Local Langlands Correspondence for GL(n,F), n a prime

In this paper, we give a new construction of the tame local Langlands correspondence for GL(n,F), n a prime, where F is a p-adic field. In the tame case, supercuspidal representations of GL(n,F) are parameterized by characters of elliptic tori, but the local Langlands correspondence is unnatural because it involves a twist by some character of the torus. Taking the cue from real groups, supercuspidal representations should instead be parameterized by characters of covers of tori. Over the reals, Harish-Chandra described the characters of discrete series restricted to compact tori. They are naturally written in terms of functions on a double cover of real tori. We write down a natural analogue of Harish-Chandra's character for GL(n,F), and show that it is the character of a unique supercuspidal representation, away from the local character expansion. This paves the way for a natural construction of the local Langlands correspondence for GL(n,F).

math.RT↗