Highest weight representations of Euclidean Kac-Moody algebras spanned by the principal subalgebra action (Q1088769)

Let G(A) be a Euclidean Kac-Moody algebra constructed by a Dynkin diagram A. In G(A) one can choose the principal subalgebra S which is an infinite-dimensional Heisenberg algebra. The study of G(A)-modules began with the construction of so-called basic modules defined by the diagram A. The basic modules have the following property: they are generated by a highest weight vector by the action of S. In this paper it is proved that in the case \(A_ n^{(1)}\), \(D_ 4^{(1)}\) and \(A_ 2^{(2)}\) only the basic modules have this property.