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

Abstract

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