2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61032We present a general vertex operator construction based on the Fock space for an affine Lie algebras of type $A$. This construction allows us to give a unified treatment for both the homogeneous and principle realizations of the affine Lie algebras $\hat{gl}_N$ as well as for some extended affine Lie algebras coordinatized by certain quantum tori.Quantum AlgebraRepresentation Theory17B10,17B69,17B60text