Hodge theory and unitary representations, in the example of $\mathrm{SL}(2,\mathbb{R})$

TL;DR

This paper explores the conjecture regarding irreducible unitary representations of reductive Lie groups, focusing on the specific case of SL(2,R), aiming to deepen understanding of their structure.

Contribution

It presents a conjecture about the classification of irreducible unitary representations of SL(2,R), contributing to the broader understanding of representation theory of reductive Lie groups.

Findings

Proposes a conjecture on the structure of unitary representations.

Provides insights into the specific case of SL(2,R).

Lays groundwork for future proofs or classifications.

Abstract

We describe our conjecture about the irreducible unitary representations of reductive Lie groups, in the special case of $\mathrm{SL}(2,\mathbb{R})$.