## Simple Whittaker modules over free bosonic orbifold vertex operator algebras

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- by Jonas T. Hartwig and Nina Yu PDF
- Proc. Amer. Math. Soc.
**147**(2019), 3259-3272 Request permission

## 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].## References

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## Additional Information

**Jonas T. Hartwig**- Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50011
- MR Author ID: 776335
- Email: jth@iastate.edu
**Nina Yu**- Affiliation: School of Mathematical Sciences, Xiamen University, Fujian, 361005, People’s Republic of China
- MR Author ID: 830351
- Email: ninayu@xmu.edu.cn
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 3259-3272 - MSC (2010): Primary 17B69
- DOI: https://doi.org/10.1090/proc/14461
- MathSciNet review: 3981106