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 F1 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 η. We are hopeful that this representation can be extended to the whole group F1, 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].
Keywords: Fischer-Griess simple group F1, Thompson series, Leech lattice, Dedekind's η-function, second quantization
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