Langlands Duality and Invariant Differential Operators

TL;DR

This paper explores the connection between Langlands duality and invariant differential operators, aiming to bridge two significant areas rooted in representation theory of semisimple Lie groups.

Contribution

It introduces a novel approach to connect Langlands duality with invariant differential operators, which were previously considered unrelated.

Findings

Establishes a theoretical link between Langlands duality and invariant differential operators.

Provides a new perspective on the role of Harish-Chandra's representation theory.

Lays groundwork for further research bridging these two areas.

Abstract

Langlands duality is one of the most influential topics in mathematical research. It has many different appearances and influential subtopics. Yet there is a topic that until now seems unrelated to the Langlands program. That is the topic of invariant differential operators. That is strange since both items are deeply rooted in Harish-Chandra's representation theory of semisimple Lie groups. In this paper we start building the bridge between the two programs.