Abstract
We consider the relationship between the conjectured uniqueness of the Moonshine Module,
, and Monstrous Moonshine, the genus zero property of the modular invariance group for each Monster group Thompson series. We first discuss a family of possibleZ n meromorphic orbifold constructions of
based on automorphisms of the Leech lattice compactified bosonic string. We reproduce the Thompson series for all 51 non-Fricke classes of the Monster groupM together with a new relationship between the centralisers of these classes and 51 corresponding Conway group centralisers (generalising a well-known relationship for 5 such classes). Assuming that
is unique, we consider meromorphic orbifoldings of
and show that Monstrous Moonshine holds if and onlyZ r if the only meromorphic orbifoldings of
are
itself or the Leech theory. This constraint on the meromorphic orbifoldings of
therefore relates Monstrous Moonshine to the uniqueness of
in a new way.
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Tuite, M.P. On the relationship between Monstrous Moonshine and the uniqueness of the Moonshine Module. Commun.Math. Phys. 166, 495–532 (1995). https://doi.org/10.1007/BF02099885
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DOI: https://doi.org/10.1007/BF02099885