2016
DOI: 10.1186/s40687-016-0084-7
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A proof of the Thompson moonshine conjecture

Abstract: In this paper, we prove the existence of an infinite-dimensional graded supermodule for the finite sporadic Thompson group Th whose McKay-Thompson series are weakly holomorphic modular forms of weight 1 2 satisfying properties conjectured by Harvey and Rayhaun.

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Cited by 18 publications
(22 citation statements)
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“…More explicitly, we proposed in Section 3 six conditions of generalised umbral moonshine conjecture and provided evidence in the form of proposing all the twistedtwined functions for all cases of generalised umbral moonshine. A proof of this conjecture should be attaianable following the methods of [32,45].…”
Section: Summary and Discussionmentioning
confidence: 99%
“…More explicitly, we proposed in Section 3 six conditions of generalised umbral moonshine conjecture and provided evidence in the form of proposing all the twistedtwined functions for all cases of generalised umbral moonshine. A proof of this conjecture should be attaianable following the methods of [32,45].…”
Section: Summary and Discussionmentioning
confidence: 99%
“…Duncan, Griffin, and the second author gave a survey [7] of the advancements in the theory of moonshine and its applications to physics as of 2015, including their proof [8] of the Umbral Moonshine Conjecture of Cheng, Duncan and Harvey [2]. Along these lines, there has been a flurry of recent work (for example, see [9,13]).…”
Section: Introduction and Statement Of Resultsmentioning
confidence: 99%
“…Schematically, they can be most naturally viewed as a sum of two contributions F 3,g = Projected Rademacher Sum + θ -corrections , (5.25) where the first term is the Rademacher sum of the unique polar term 2q −3 for the suitable group Γ g and multiplier system, projected onto the Kohnen plus space, and the second term again involves linear combinations of θ (d 2 τ), where d are certain integers compatible with the group Γ g . We refer to [99], and in particular [104] for more details.…”
Section: Thompson Moonshinementioning
confidence: 99%