A Class Of Irreducible A₁^（1）-modules

Let α∈C. For any irreducible module V over the two dimensional non-abelian Lie algebra b, we define a class of weight modules Fα(V) over the affine Lie algebra A1(1). These weight modules have infinite dimensional weight spaces if dimV>1. In this paper, we will determine the necessary and sufficient conditions for these modules F"(V) to be irreducible. In this way we obtain a lot of irreducible weight A1(1)-modules with infinite dimensional weight spaces.