Abstract
We use the underlying Fock space for the homogeneous vertex operator representation of the affine Lie algebra to construct a family of vertex operators. As an application, an irreducible module for an extended affine Lie algebra of type A N −1 coordinatized by a quantum torus ℂ q of 2 variables (or 3 variables) is obtained. Moreover, this module turns out to be a highest weight module which is an analog of the basic module for affine Lie algebras.
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