Proof of the Umbral Moonshine Conjecture
Representation Theory
2015-12-31 v2 Number Theory
Abstract
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.
Keywords
Cite
@article{arxiv.1503.01472,
title = {Proof of the Umbral Moonshine Conjecture},
author = {John F. R. Duncan and Michael J. Griffin and Ken Ono},
journal= {arXiv preprint arXiv:1503.01472},
year = {2015}
}
Comments
56 pages, to appear in Research in the Mathematical Sciences