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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Abstract

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:	14 Dec 2022 14:59
URI:	https://dair.dias.ie/id/eprint/734

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