Mathematical Research Letters

Volume 23 (2016)

Number 3

Rectifiers and the local Langlands correspondence: the unramified case

Pages: 593 – 619

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n3.a1

Authors

Moshe Adrian (Department of Mathematics, University of Toronto, Ontario, Canada)

David Roe (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)

Abstract

Bushnell and Henniart define rectifiers, which provide a correction term in the local Langlands correspondence for $\mathrm{GL}_n(K)$. They also give a natural bijection between essentially tame supercuspidal Langlands parameters and characters of minisotropic tori, and a second bijection between characters of minisotropic tori and supercuspidal representations of $\mathrm{GL}_n(K)$. Rectifiers bridge the gap, adding an intermediate step so that the composition agrees with the local Langlands correspondence. In this paper, we begin the process of generalizing rectifiers to other connected reductive groups, focusing on the case of unramified minisotropic tori that satisfy a certain cohomology condition.

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