Proof of the umbral moonshine conjecture

@article{Duncan2015ProofOT,
  title={Proof of the umbral moonshine conjecture},
  author={J. Duncan and Michael Griffin and K. Ono},
  journal={Research in the Mathematical Sciences},
  year={2015},
  volume={2},
  pages={1-47}
}
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. 
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