New representations of affine Kac-Moody algebras

Abstract

Let h˜ be a Cartan subalgebra of an affine Kac-Moody algebra without containing the center. In this paper, we classify the module structures on U(h˜) for all affine Kac-Moody algebras which are free U(h˜)-modules of rank 1. These modules exist only for type Al(1)(l≥1) or Cl(1)(l≥2) affine Kac-Moody algebras, they are generically non-weight and simple. Hence, we obtain a class of new simple modules over these affine Kac-Moody algebras.