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
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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].

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