Admissible embedding of L-groups and essentially tame local Langlands correspondence

TL;DR

This paper offers a new interpretation of the essentially tame local Langlands correspondence for GL_n over non-Archimedean fields, using admissible embeddings of L-groups to describe Langlands parameters of supercuspidal representations.

Contribution

It introduces a novel perspective on the correspondence by leveraging admissible embeddings, building on previous work to clarify the parameterization of supercuspidal representations.

Findings

Describes Langlands parameters via admissible embeddings

Provides a reinterpretation of Bushnell and Henniart's correspondence

Connects admissible embeddings with supercuspidal representations

Abstract

Let $F$ be a non-Archimedean local field and $G$ be the general linear group $\mathrm{GL}_n$ over $F$. Based on the previous results of the author, we can describe the Langlands parameter of an essentially tame supercuspidal representation of $G(F)$ by those admissible embeddings of L-groups constructed by Langlands and Shelstad. We therefore provide a different interpretation on Bushnell and Henniart's essentially tame local Langlands correspondence.