Abstract
In this paper, we consider the imaginary highest weight modules and the imaginary Whittaker modules for the affine Nappi—Witten algebra. We show that simple singular imaginary Whittaker modules at level (κ, c)(κ ∈ ℂ✭) are simple imaginary highest weight modules. The necessary and sufficient conditions for these imaginary modules to be simple are given. All simple imaginary modules are classified.
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The authors would like to thank the referee for valuable suggestions to improve the paper.
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Supported by NSF of China (Grant Nos. 11801117, 11801390), the Natural Science Foundation of Guangdong Province, China (Grant No. 2018A030313268) and the General Finacial Grant from the China Postdoctoral Science Foundation (Grant No. 2016M600140)
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Bao, Y.X., Cai, Y.A. Imaginary Modules over the Affine Nappi—Witten Algebra. Acta. Math. Sin.-English Ser. 38, 1041–1053 (2022). https://doi.org/10.1007/s10114-022-0246-z
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DOI: https://doi.org/10.1007/s10114-022-0246-z
Keywords
- Affine Nappi—Witten algebra
- imaginary Verma modules
- imaginary highest weight modules
- imaginary Whittaker modules
- simple modules