Representations of affine Nappi-Witten algebras

TL;DR

This paper classifies irreducible modules and constructs Wakimoto modules for the affine Nappi-Witten algebra, providing a detailed understanding of its representation theory and module structure.

Contribution

It introduces a complete classification of irreducible highest weight modules and constructs Wakimoto modules for the affine Nappi-Witten algebra, linking to vertex operator algebra theory.

Findings

Classification of all irreducible highest weight modules

Necessary and sufficient conditions for module irreducibility

Construction of Wakimoto type modules

Abstract

In this paper, we study the representation theory for the affine Lie algebra $\H$ associated to the Nappi-Witten model $H_{4}$. We classify all the irreducible highest weight modules of $\H$. Furthermore, we give a necessary and sufficient condition for each $\H$-(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.