2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62546In this paper, we study the algebra of twisted vertex operators over an even integral ${\mathbf Z}_2$-lattice, and give a kind of systematic construction of fundamental representations for affine Lie algebras of type $A$, $D$, $E$ with their irreducible decompositions.29 pages, AMS-LatexRepresentation Theory17B67 (Primary) 17B69 (Secondary)text