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Simple Whittaker modules over free bosonic orbifold vertex operator algebras


Authors: Jonas T. Hartwig and Nina Yu
Journal: Proc. Amer. Math. Soc. 147 (2019), 3259-3272
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/proc/14461
Published electronically: March 26, 2019
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Abstract: We construct weak (i.e. nongraded) modules over the vertex operator algebra $ M(1)^+$, which is the fixed-point subalgebra of the higher rank free bosonic (Heisenberg) vertex operator algebra with respect to the $ -1$ automorphism. These weak modules are constructed from Whittaker modules for the higher rank Heisenberg algebra. We prove that the modules are simple as weak modules over $ M(1)^+$ and calculate their Whittaker type when regarded as modules for the Virasoro Lie algebra. Lastly, we show that any Whittaker module for the Virasoro Lie algebra occurs in this way. These results are a higher rank generalization of some results by Tanabe [Proc. Amer. Math. Soc. 145 (2017), no. 10, pp. 4127-4140].


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Additional Information

Jonas T. Hartwig
Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email: jth@iastate.edu

Nina Yu
Affiliation: School of Mathematical Sciences, Xiamen University, Fujian, 361005, People’s Republic of China
Email: ninayu@xmu.edu.cn

DOI: https://doi.org/10.1090/proc/14461
Received by editor(s): July 11, 2018
Received by editor(s) in revised form: November 4, 2018
Published electronically: March 26, 2019
Additional Notes: The second author was supported by China NSF 11601452, Fundamental Research Funds for the Central Universities 20720170010, and Research Fund for Fujian Faculty JAT170006
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2019 American Mathematical Society