Classification of irreducible integrable modules for extended affine Lie algebras with center acting trivially

TL;DR

This paper classifies irreducible integrable modules for a specific class of extended affine Lie algebras, showing they are highest weight modules with trivial central action, advancing understanding of their representation theory.

Contribution

It provides a complete classification of such modules, proving the triviality of the central extension action and characterizing modules as highest weight modules.

Findings

Central extension acts trivially on modules

Modules are highest weight modules

Classification completes understanding of these modules' structure

Abstract

We classify the irreducible integrable modules for the twisted toroidal extended affine Lie algebras with fnite diemnsional weight spaces where the fnite dimensional center acts trivially. We have proved that the entire central extension part acts trivially on the modules and our modules turn out to be highest weight modules.