The Local Langlands Correspondence for Simple Supercuspidal Representations of GL_n(F)

Abstract

Let F be a non-archimedean local field of characteristic zero with residual characteristic p. In this paper, we present a simple proof and construction of the local Langlands correspondence for simple supercuspidal representations of GL_n(F), when p does not divide n. As an application, we prove Jacquet's conjecture on the local converse problem for GL_n(F) in the case of simple supercuspidal representations, for arbitrary p.