Classification of irreducible integrable highest weight modules for current Kac-Moody Algebras

TL;DR

This paper classifies irreducible, integrable highest weight modules for current Kac-Moody algebras, showing they are essentially modules over direct sums of finitely many Kac-Moody Lie algebras, with finite-dimensional weight spaces.

Contribution

It provides a complete classification of such modules, revealing their structure as modules over direct sums of Kac-Moody Lie algebras.

Findings

Modules are modules of direct sums of finitely many Kac-Moody Lie algebras

Modules have finite-dimensional weight spaces

Classification is complete for irreducible, integrable highest weight modules

Abstract

This paper classifies irreducible, integrable highest weight modules for "current Kac-Moody Algebras" with finite dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many copies of Kac-Moody Lie algebras.