A proof of the Thompson Moonshine Conjecture

Michael J. Griffin; Michael H. Mertens

doi:10.1186/s40687-016-0084-7

A proof of the Thompson Moonshine Conjecture

Number Theory 2020-07-02 v2 Representation Theory

Authors: Michael J. Griffin , Michael H. Mertens

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Abstract

In this paper we prove the existence of an infinite dimensional graded super-module for the finite sporadic Thompson group $Th$ whose McKay-Thompson series are weakly holomorphic modular forms of weight $\frac 12$ satisfying properties conjectured by Harvey and Rayhaun.

Keywords

Thompson moonshine conjecture Thompson group graded super-module McKay-Thompson series weakly holomorphic modular forms modular forms of weight 1/2 finite sporadic group

Cite

@article{arxiv.1607.03078,
  title  = {A proof of the Thompson Moonshine Conjecture},
  author = {Michael J. Griffin and Michael H. Mertens},
  journal= {arXiv preprint arXiv:1607.03078},
  year   = {2020}
}

Comments

36 pages, 8 tables v2 addresses reviewer's comments and corrects a mistake in the proof of Lemma 2.10

A proof of the Thompson Moonshine Conjecture

Abstract

Keywords

Cite

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