Langlands parameters for epipelagic representations of $\text{\rm GL}_n$

TL;DR

This paper provides a complete explicit description of the Langlands parameters for epipelagic representations of GL_n over non-Archimedean local fields, focusing on those with Swan conductor equal to 1.

Contribution

It offers a full and explicit characterization of Langlands parameters specifically for epipelagic representations of GL_n, advancing understanding in local Langlands correspondence.

Findings

Explicit description of Langlands parameters for epipelagic representations

Classification of such representations with Swan conductor 1

Enhanced understanding of local Langlands correspondence for these cases

Abstract

Let $F$ be a non-Archimedean local field. An irreducible cuspidal representation of $\text{\rm GL}_n(F)$ is epipelagic if its Swan conductor equals 1. We give a full and explicit description of the Langlands parameters of such representations.