On an explicit isomorphism of standard level-one modules for \(\hat D_{4n}\) (Q1355582)

This paper forms part of the program of finding alternative constructions of the Monster simple group. The affine Kac-Moody algebra of type \(\hat D_{4n} \) has four non-isomorphic irreducible highest-weight modules of level 1. Using vertex operator techniques, the idea of the paper is to construct a set of twisted forms of the algebra and give an explicit description of the four irreducible modules for each algebra. The author gives isomorphisms between the algebras and explicit graded isomorphisms between the matching pairs of modules. Using this explicit isomorphism, one may then give a \(Z_6\)-orbifold construction of the Monster for the affine algebra associated to a direct sum of six copies of \(D_{4}\).