An informal introduction to categorical representation theory and the local geometric Langlands program

TL;DR

This paper offers an accessible overview of categorical representation theory and the local geometric Langlands program, highlighting their applications to classical and affine Lie algebra representation theory.

Contribution

It introduces the concepts of categorical actions and the local geometric Langlands program with a focus on their applications, bridging classical and modern representation theories.

Findings

Connections between categorical actions and Lie algebra representations

New insights into the local geometric Langlands correspondence

Applications to reductive and affine Lie algebra representation theory

Abstract

We provide a motivated introduction to the theory of categorical actions of groups and the local geometric Langlands program. Along the way we emphasize applications, old and new, to the usual representation theory of reductive and affine Lie algebra