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arXiv · 1710.00737

A Self-Dual Integral Form of the Moonshine Module

Scott Carnahan
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Abstract

We construct a self-dual integral form of the moonshine vertex operator algebra, and show that it has symmetries given by the Fischer-Griess monster simple group. The existence of this form resolves the last remaining open assumption in the proof of the modular moonshine conjecture by Borcherds and Ryba. As a corollary, we find that Griess's original 196884-dimensional representation of the monster admits a positive-definite self-dual integral form with monster symmetry.

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BibTeXRIS

Scott Carnahan. 2017-10-02. A Self-Dual Integral Form of the Moonshine Module. https://doi.org/10.3842/sigma.2019.030

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