A proof of the Thompson Moonshine Conjecture

TL;DR

This paper proves the existence of a special infinite-dimensional graded super-module for the Thompson group, with McKay-Thompson series that are weakly holomorphic modular forms, confirming conjectures by Harvey and Rayhaun.

Contribution

It establishes the existence of a new mathematical structure linking the Thompson group to modular forms, confirming conjectured properties.

Findings

Existence of an infinite-dimensional graded super-module for Th

McKay-Thompson series are weakly holomorphic modular forms

Properties conjectured by Harvey and Rayhaun are verified

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.