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Lie Group Quantum Mathematics Seminar

Moonshine modules and a question of Griess

Lea Beneish, University of North Texas

Location:  Zoom (see below for the zoom link)
Date & time: Friday, 22 March 2024 at 12:10PM - 1:10PM

Recent work on monstrous moonshine has shown that there are exact formulas for the multiplicities of the irreducible components of the moonshine modules, showing in particular that these multiplicities are asymptotically proportional to the dimensions. With the recent proof of the umbral moonshine conjecture it is natural to ask whether this distribution result extends to other instances of moonshine, including umbral moonshine. We consider the general 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 some mild hypotheses 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. This talk is based on joint work with Victor Manuel Aricheta.


Zoom link:

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