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

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.

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