Representations of affine Nappi-Witten algebras

In this paper, we study the representation theory for the affine Lie algebra (H) over cap (4) associated to the Nappi-Witten model (H) over cap (4). We classify all the irreducible highest weight modules of (H) over cap (4). Furthermore, we give a necessary and sufficient condition for each (H) over cap (4)-(generalized) Verma module to be irreducible. For reducible ones, we characterize all the linearly independent singular vectors. Finally, we construct Wakimoto type modules for these Lie algebras and interpret this construction in terms of vertex operator algebras and their modules. (C) 2011 Elsevier Inc. All rights reserved.