An Overview of Penumbral Moonshine
arXiv:2109.09756
Abstract
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.
96 pages, 55 tables, small typos corrected, tables reformatted