Localization of highest weight modules of a class of Extended Affine Lie Algebras

TL;DR

This paper applies localization techniques to free field realizations of highest weight modules over extended affine Lie algebras, constructing new simple weight modules with infinite weight multiplicities and establishing irreducibility conditions.

Contribution

It introduces a novel application of localization to existing free field realizations, creating new classes of simple weight modules for extended affine Lie algebras.

Findings

Constructed new weight modules via localization.

Provided necessary and sufficient conditions for irreducibility.

Realized free field representations for modules with infinite weight multiplicities.

Abstract

In 2006, Gao and Zeng \cite{GZ} gave the free field realizations of highest weight modules over a class of extended affine Lie algebras. In the present paper, applying the technique of localization to those free field realizations, we construct a class of new weight modules over the extended affine Lie algebras. We give necessary and sufficient conditions for these modules to be irreducible. In this way, we construct free field realizations for a class of simple weight modules with infinite weight multiplicities over the extended affine Lie algebras.