Classification of integrable representations for toroidal extended affine Lie algebras

TL;DR

This paper classifies irreducible integrable modules with finite-dimensional weight spaces for nullity 2 toroidal extended affine Lie algebras, advancing understanding of their representation theory.

Contribution

It provides a complete classification of such modules, focusing on the core action and nullity 2 case, which was previously not fully understood.

Findings

Classification of irreducible integrable modules achieved

Finite-dimensional weight spaces characterized

New insights into the structure of toroidal extended affine Lie algebras

Abstract

In this paper, we classify the irreducible integrable modules with finite dimensional weight spaces and non-trivial $\widetilde{\mathfrak g}_c$-action for the nullity $2$ toroidal extended affine Lie algebra $\widetilde{\mathfrak g}$, where $\widetilde{\mathfrak g}_c$ is the core of $\widetilde{\mathfrak g}$.