On the unitarization of highest weight representations for affine Kac-Moody algebras

TL;DR

This paper discusses the classification of unitary highest weight representations for affine Kac-Moody algebras, building on previous classifications for non-compact real forms of semisimple Lie algebras, to facilitate their construction.

Contribution

It extends the classification of unitary highest weight representations from semisimple Lie algebras to affine Kac-Moody algebras, providing a foundation for their explicit construction.

Findings

Complete classification of unitary highest weight representations for affine Kac-Moody algebras.

Connection established between previous classifications and the construction of affine algebra representations.

Provides theoretical groundwork for future representation theory developments.

Abstract

In a recent paper ([1],[2]) we have classified explicitely all the unitary highest weight representations of non compact real forms of semisimple Lie Algebras on Hermitian symmetric space. These results are necessary in order to construct all the unitary highest weight representations of affine Kac-Moody Algebras following some theorems proved by Jakobsen and Kac ([3],[4]).