Representations of the twisted affine Nappi-Witten algebras

Abstract

In this paper, we study Verma modules for the twisted affine Nappi-Witten algebras \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{1}]$\end{document}Ĥ4[τ1] and \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{2}]$\end{document}Ĥ4[τ2]. The vertex operator representations of the affine Nappi-Witten algebras \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{1}]$\end{document}Ĥ4[τ1], \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}[\tau _{2}]$\end{document}Ĥ4[τ2], and \documentclass[12pt]{minimal}\begin{document}$\widehat{H}_{4}$\end{document}Ĥ4 are also constructed. Furthermore, the irreducible non-zero level quasifinite modules over the affine Nappi-Witten algebras are classified.

Whittaker modules for the twisted affine Nappi-Witten Lie algebra Hˆ4[τ]

“…In the following we consider the case that ψ is identically zero. We first recall the definition of Verma module for the twisted affine Nappi-Witten Lie algebra H 4 [τ ] given in [8]. If ψ is identically zero, for l ∈ C, let Then (i) M i is a Whittaker submodule of L 0,ξ , with a cyclic Whittaker vector ω i = ((a + b)(0) − l) iω , and M i+1 is a maximal submodule of M i ;…”

“…The irreducible restricted modules for H 4 with some natural conditions have been classified and the extension of the vertex operator algebra V H 4 (l, 0) by the even lattice L has been considered in [10]. Verma modules and vertex operator representations for the twisted affine Nappi-Witten Lie algebra H 4 [τ ] have also been investigated in [8].…”

“…The irreducible restricted modules for H 4 with some natural conditions have been classified and the extension of the vertex operator algebra V H 4 (l, 0) by the even lattice L has been considered in [10]. Verma modules and vertex operator representations for the twisted affine Nappi-Witten Lie algebra H 4 [τ ] have also been investigated in [8].Whittaker modules were originally introduced by D. Arnal and G. Pinczon [2] in the construction of a very vast family of representations for sl(2). A class of Whittaker modules for an arbitrary finite-dimensional complex semisimple Lie algebra g were defined…”