A Class of Irreducible Modules for the Extended Affine Lie Algebra $\widetilde{\frak{gl}_l({\mathbb{C}_q})}$

TL;DR

This paper constructs a new class of modules for the extended affine Lie algebra $ ilde{rak{gl}_l(c_q)}$ using free fields and provides criteria for their irreducibility.

Contribution

It introduces a novel construction of modules for the algebra and establishes a complete criterion for their irreducibility.

Findings

Constructed a new class of modules for $ ilde{rak{gl}_l(c_q)}$

Derived necessary and sufficient conditions for irreducibility

Utilized free fields in the module construction

Abstract

We construct a class of modules for extended affine Lie algebra $\widetilde{\frak{gl}_l({\bc_q})}$ by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.