New representations of affine Kac-Moody algebras

Let (h) over tilde 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) over tilde) for all affine Kac-Moody algebras which are free U((h) over tilde)-modules of rank 1. These modules exist only for type A(l)((1))(l >= 1) or C-l((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. (C) 2019 Elsevier Inc. All rights reserved.