A unified view of some vertex operator constructions
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affinealgebrasconstructionoperatorsomeunifiedvertexallows
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We 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.
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