# 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.

## Key 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 $\widetilde{\mathfrak g}$.