2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106060We use the idea of free fields to obtain highest weight representations for the extended affine Lie algebra $\widetilde{\frak{gl}_{2}(\bc_q)}$ coordinatized by the quantum torus $\bc_q$ and go on to construct a contravariant hermitian form. We further give a necessary and sufficient condition such that the contravariant hermitian form is positive definite.24 pagesRepresentation TheoryQuantum Algebra16G30text