Simple Whittaker modules over free bosonic orbifold vertex operator algebras

Hartwig, Jonas; Yu, Nina

doi:10.1090/proc/14461

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
MathSciNet review: 3981106
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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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