Integrable Modules of Map full Toroidal Lie Algebras

TL;DR

This paper classifies irreducible integrable modules with finite-dimensional weight spaces for Map full Toroidal Lie algebras, showing they are evaluation modules and thus providing a clear structure for these representations.

Contribution

It characterizes the irreducible integrable modules of Map full Toroidal Lie algebras as evaluation modules, clarifying their structure and classification.

Findings

Irreducible integrable modules are single point evaluation modules.

These modules have finite-dimensional weight spaces.

The modules are irreducible for the underlying full toroidal algebras.

Abstract

In this paper, we study the irreducible objects of the category Cf in of integrable representations for Map full Toroidal Lie algebras with finite dimensional weight spaces. These representations turn out to be single point evaluation modules and hence are irreducible-integrable modules for the underlying full toroidal algebras.