Monstrous Moonshine and the Uniqueness of the Moonshine Module

Tuite, Michael P. (1992) Monstrous Moonshine and the Uniqueness of the Moonshine Module. (Preprint)

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In this talk we consider the relationship between the conjectured uniqueness of the Moonshine module V♮ of Frenkel, Lepowsky and Meurman and Monstrous Moonshine, the genus zero property for Thompson series discovered by Conway and Norton. We discuss some evidence to support the uniqueness of V♮ by considering possible alternative orbifold constructions of V♮ from a Leech lattice compactified string. Within these constructions we find a new relationship between the centralisers of the Monster group and the Conway group generalising an observation made by Conway and Norton. We also relate the uniqueness of V♮ to Monstrous Moonshine and argue that given this uniqueness, then the genus zero properties hold if and only if orbifolding V♮ with respect to a monster element reproduces V♮ or the Leech theory.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 14:13
Last Modified: 19 Jul 2018 13:07

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