Integrability of weight modules of degree 1

TL;DR

This paper classifies all weight modules of degree 1 for simple complex Lie algebras that can be integrated into continuous Hilbert space representations of corresponding real Lie groups.

Contribution

It provides a complete classification of integrable weight modules of degree 1 for simple complex Lie algebras, linking algebraic modules to group representations.

Findings

Identifies all degree 1 weight modules integrable to real Lie group representations.

Establishes criteria for integrability of these modules.

Connects algebraic module theory with continuous group representations.

Abstract

The aim of this article is to find all weight modules of degree 1 of a simple complex Lie algebra that integrate to a continuous representation of a simply-connected real Lie group on some Hilbert space.