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arXiv · 2202.08271

Modular Products and Modules for Finite Groups

John F. R. Duncan·Jeffrey A. Harvey·Brandon C. Rayhaun
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Abstract

Motivated by the appearance of penumbral moonshine, and by evidence that penumbral moonshine enjoys an extensive relationship to generalized monstrous moonshine via infinite products, we establish a general construction in this work which uses singular theta lifts and a concrete construction at the level of modules for a finite group to translate between moonshine in weight one-half and moonshine in weight zero. This construction serves as a foundation for a companion paper in which we explore the connection between penumbral Thompson moonshine and a special case of generalized monstrous moonshine in detail.

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BibTeXRIS

John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun. 2022-02-16. Modular Products and Modules for Finite Groups. https://arxiv.org/abs/2202.08271

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