Imaginary modules over the affine Nappi-Witten algebra (Q2150681)

The Nappi-Witten Lie algebra \(H_4\) is a four dimensional vector space \[ H_4= \mathbb{C}a\oplus \mathbb{C}b\oplus\mathbb{C}c\oplus\mathbb{C}d \] equipped with the bracket relations \([a, b]=c, [d, a]=a, [d, b]=-b, [c, H_4]=0\). The affine Nappi-Witten Lie algebra \(\hat{H}_4\) is defined to be the central extension of the loop algebra of \(H_4\). In this paper, the authors introduced the imaginary highest weight modules and the imaginary Whittaker modules for the affine Nappi-Witten algebra. They studied the simplicity of imaginary modules and gave a classification of these simple imaginary modules. They also showed that simple singular imaginary Whittaker modules at level \((k,c)(k\in \mathbb{C}^*)\) are simple imaginary highest weight modules.