Representations of reductive groups over local fields

TL;DR

This paper reviews recent progress in classifying irreducible admissible representations of reductive groups over local fields and explores aspects of the local Langlands correspondence, including some conjectural compatibility properties.

Contribution

It summarizes advances in the classification of representations and discusses conjectural compatibility properties of the local Langlands correspondence.

Findings

Progress in classifying irreducible admissible representations

Discussion of conjectural compatibility properties

Overview of the local Langlands correspondence

Abstract

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility properties of the refined local Langlands correspondence.