2022/02/16 by John F. R. Duncan, Jeffrey A. Harvey, Duncan, John F. R. +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.2202.08271
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.