2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77963We present a vertex operator algebra which is an extension of the level $k$ vertex operator algebra for the $\hat{sl}_2$ conformal field theory. We construct monomial basis of its irreducible representations.To appear in the Festschrift in honor of Prof. McGuire published by World Scientific PC. In the present version several corrections are madeQuantum AlgebraRepresentation Theorytext