Classification of irreducible integrable representations of loop toroidal Lie algebras

TL;DR

This paper classifies irreducible integrable representations of loop toroidal Lie algebras, detailing modules with both trivial and non-trivial center actions, advancing understanding of their structure.

Contribution

It provides a comprehensive classification of such representations, including cases with different center actions, which was previously not fully understood.

Findings

Classification of modules with non-trivial center action

Classification of modules with trivial center action

Enhanced understanding of the structure of loop toroidal Lie algebra representations

Abstract

In this paper we classify irreducible integrable representations of loop toroidal Lie algebras with finite dimensional weight spaces. In both the cases we classify modules, when a part of center acts non-trivially and trivially on modules.