An Overview of Penumbral Moonshine

20 Sep 2021 · John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun ·

As Mathieu moonshine is a special case of umbral moonshine, Thompson moonshine (in half-integral weight) is a special case of a family of similar relationships between finite groups and vector-valued modular forms of a certain kind. We call this penumbral moonshine. We introduce and explain some features of this phenomenon in this work.