Classification of level zero irreducible integrable modules for twisted full toroidal Lie algebras

TL;DR

This paper classifies all irreducible integrable modules with finite-dimensional weight spaces for twisted full toroidal Lie algebras, extending the understanding of their representation theory in the context of multiloop algebra automorphisms.

Contribution

It provides a complete classification of certain modules for twisted full toroidal Lie algebras, a significant step in their representation theory.

Findings

Complete classification of irreducible integrable modules

Modules have finite-dimensional weight spaces

Centre acts trivially in classified modules

Abstract

In this paper, we first construct the twisted full toroidal Lie algebra by an extension of a centreless Lie torus $LT$ which is a multiloop algebra twisted by several automorphisms of finite order and equipped with a particular grading. We then provide a complete classification of all the irreducible integrable modules with finite dimensional weight spaces for this twisted full toroidal Lie algebra having a non-trivial $LT$-action and where the centre of the underlying Lie algebra acts trivially.