Representations of loop extended Witt algebras

TL;DR

This paper classifies irreducible modules of loop extended Witt algebras, showing they are either bounded or highest weight modules, and are all evaluation modules for extended Witt algebras.

Contribution

It provides a complete classification of irreducible modules with finite dimensional weight spaces for loop extended Witt algebras, identifying their structure as evaluation modules.

Findings

Irreducible modules are either bounded or highest weight.

All such modules are single point evaluation modules.

These modules are irreducible modules for extended Witt algebras.

Abstract

In this paper, we classify irreducible modules for loop extended Witt algebras with finite dimensional weight spaces. They turn out to be either modules with uniformly bounded weight spaces or highest weight modules. We further prove that all these modules are single point evaluation modules ($n \geq 2$). So they are actually irreducible modules for extended Witt algebras.