Vertex operators arising from the homogeneous realization for \(\widehat{\text{gl}}_N\)
The author uses the underlying Fock space for the homogeneous vertex operator representation of the affine Lie algebra \(\widehat{gl}_N\) to construct a family of vertex operators. As an application he obtains an irreducible module for an extended affine Lie algebra of type \(A_{N-1}\) coordinated by a quantum torus in 2 or 3 variables. It turns out that this module is a highest weight module, which is an analogue of the basic module for affine Lie algebras. The paper contains a lot of technicalities.
scientific article; zbMATH DE number 1520501