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

The Whittaker module $M_{\psi }$ and its quotient Whittaker module $L_{\psi, \xi}$forthetwistedaffineNappi-WittenLiealgebra$\widehat{H}{4}[\tau]$arestudied\mathrm{.}Fornonsingulartype,itisprovedthatif$\xi\neq 0$,then$L{\psi,\xi}$isirreducibleandanyirreducibleWhittaker$\widehat{H}_{4}[\tau]$-moduleoftype$\psi$with${\bf k}$ 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 $\xi \mathrm{\ne }0$ are fully characterized.