A remark on the Conway-Norton conjecture about the “Monster” simple group

Abstract

By the method of second quantization we construct an infinite-dimensional graded module for the centralizer of an involution of the Fischer-Griess "Monster" simple group F(1) so that the Thompson series are those conjectured by Conway and Norton. As a consequence we obtain some identities and congruences relating modular functions j and eta. We are hopeful that this representation can be extended to the whole group F(1), proving all the conjectures by Conway and Norton in their recent paper [Conway, J. H. & Norton, S. P. (1979) Bull. London Math. Soc. 11, 308-339].