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

TL;DR

This paper provides a straightforward proof of the local Langlands correspondence for simple supercuspidal representations of GL_n(F) when p does not divide n, and confirms Jacquet's conjecture for these cases.

Contribution

It introduces a simplified construction of the local Langlands correspondence specifically for simple supercuspidal representations of GL_n(F).

Findings

Proof of the local Langlands correspondence for simple supercuspidal representations.

Verification of Jacquet's conjecture for these representations across all p.

A new, simplified approach to understanding supercuspidal representations.

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.