Abstract
The Nappi-Witten Lie algebra was first introduced by C. Nappi and E. Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave. The associated Lie algebra is neither abelian nor semisimple. Recently K. Christodoulopoulou studied the irreducible Whittaker modules for finite- and infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules. In this paper, imaginary Whittaker modules of the twisted affine Nappi-Witten Lie algebra are constructed based on Whittaker modules of Heisenberg algebras. It is proved that the imaginary Whittaker module with the center acting as a non-zero scalar is irreducible.
Highlights
The conform field theory (CFT) plays an important role in mathematics and physics
Witten in the study of Wess-Zumino-Novikov-Witten (WZNW) models. They showed that the WZNW model (NW model) based on a central extension of the two-dimensional Euclidean group describes the homogeneous four-dimensional space-time corresponding to a gravitational plane wave
Christodoulopoulou studied the irreducible Whittaker modules for finiteand infinite-dimensional Heisenberg algebras and for the Lie algebra obtained by adjoining a degree derivation to an infinite-dimensional Heisenberg algebra, and used these modules to construct a new class of modules for non-twisted affine algebras, which are called imaginary Whittaker modules
Summary
The conform field theory (CFT) plays an important role in mathematics and physics. Current algebra [1] [2] has proved to be a valuable tool in understanding CFT and String Theory. The Nappi-Witten model is a WZW model based on a non-semisimple group. The twisted affine Nappi-Witten Lie algebra is defined as follows:. The representation theory for the non-twisted affine Nappi-Witten Lie algebra has been well studied in [14]. The irreducible restricted modules for the non-twisted affine Nappi-Witten Lie algebra with some natural conditions have been classified and the extension of the vertex operator algebra VH4 (l,0) by the even lattice L has been considered in [15]. [18] studied virtual Whittaker modules of the non-twisted affine Nappi-Witten Lie algebra. Inspired by the works mentioned above, the aim of the present paper is to give a characterization of the imaginary Whittaker modules for the twisted affine Nappi-Witten Lie algebra n w[θ ]. All linear spaces and algebras in this paper are over unless indicated otherwise
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