The Monster Module
It was subsequently shown by A. Oliver L. Atkin, Paul Fong and Stephen D. Smith, using computer calculation, that there is indeed an infinite-dimensional graded representation of the Monster group whose McKay-Thompson series are precisely the Hauptmoduls found by Conway and Norton. Igor Frenkel, James Lepowsky and Arne Meurman explicitly constructed this representation using vertex operators in conformal field theory, describing bosonic string theory compactified on a 24-dimensional torus generated by the Leech lattice, and orbifolded by a reflection. The resulting module is called the Monster module.
Read more about this topic: Monstrous Moonshine
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