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arXiv:1503.01472math.RT

Proof of the Umbral Moonshine Conjecture

John F. R. Duncan, Michael J. Griffin, Ken Ono

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.

arXiv comments
56 pages, to appear in Research in the Mathematical Sciences
Journal reference
Research in the Mathematical Sciences (2015) 2:26
DOI
Subjects
math.RTRepresentation Theory math.NTNumber Theory

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Linked by 2 identifiable commenters in 2 comments across 2 threads, from Apr 2015 to Apr 2018.

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  1. Mathematicians Chase Moonshine’s Shadow (2015) 1 comment

    • I get the idea that the article (which I already read some years aog, probably because it was mentioned here) just describes the route to the article "Proof of the Umbral Moonshine Conjecture", for which a pre-print appeared on https://arxiv.org/abs/1503.01472 For many…

      fjfaaseView on HNParent context

  2. A mysterious connection between number theory, algebra and string theory? 1 comment

    • The first equation on page 8 of the arXiv paper http://arxiv.org/abs/1503.01472 seems strange to me. It looks like saying "function F(t) given by F(t) + Sum(something)." Shouldn't it use ':=' symbol instead of '+', like "F(t) := Sum(something)"? Or maybe this is the case when…

      AlexCyrlexView on HNParent context

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