Whittaker modules for the twisted affine Nappi-Witten Lie algebra ${\hat{H}}_4[\tau ]$

Abstract

The Whittaker module $M_{\psi }$ and its quotient Whittaker module $L_{\psi ,\xi }$ for the twisted affine Nappi-Witten Lie algebra ${\hat{H}}_4[\tau ]$ are studied. For nonsingular type, it is proved that if $\xi \ne 0$, then $L_{\psi ,\xi }$ is irreducible and any irreducible Whittaker ${\hat{H}}_4[\tau ]$-module of type $\psi$ with $\mathbf{k}$ acting as a non-zero scalar $\xi$ is isomorphic to $L_{\psi ,\xi }$. Furthermore, for $\xi =0$, all Whittaker vectors of $L_{\psi ,0}$ are completely determined. For singular type, the Whittaker vectors of $L_{\psi ,\xi }$ with $\xi \ne 0$ are fully characterized.