The McKay-Thompson series associated with the irreducible characters of the Monster

Abstract

Let $\mathbb{V}={\coprod }_{h=0}^{\infty }{\mathbb{V}}_h$ be the graded monster module of the monster simple group $\mathbb{M}$ and let ${\chi }_k$ be an irreducible representation of $\mathbb{M}$. The generating function of $c_{hk}$ (the multiplicity of ${\chi }_k$ in ${\mathbb{V}}_h$) is determined. Furthermore, the invariance group of the modular function associated with the generating function is also determined in this paper.

arXiv comment19 pages, latex file