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arXiv · 1610.01689

Moonshine modules and a question of Griess

Victor Manuel Aricheta·Lea Beneish
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Abstract

We consider the situation in which a finite group acts on an infinite-dimensional graded module in such a way that the graded trace functions are weakly holomorphic modular forms. Under a mild hypothesis we completely describe the asymptotic module structure of the homogeneous subspaces. As a consequence we find that moonshine for a group gives rise to partial orderings on its irreducible representations. This serves as a first answer to a question posed by Griess. In particular, we show that our hypothesis holds for umbral moonshine and for automorphism groups of certain vertex operator algebras.

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Victor Manuel Aricheta, Lea Beneish. 2016-10-05. Moonshine modules and a question of Griess. https://arxiv.org/abs/1610.01689

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