Open AccessA remark on the Conway-Norton conjecture about the “Monster” simple group
Author(s) -
Victor G. Kač
Publication year - 1980
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.77.9.5048
Subject(s) - centralizer and normalizer , mathematics , monster , conjecture , simple group , involution (esoterism) , combinatorics , simple (philosophy) , algebra over a field , group (periodic table) , congruence relation , pure mathematics , physics , philosophy , epistemology , quantum mechanics , consciousness
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 groupF 1 so that the Thompson series are those conjectured by Conway and Norton. As a consequence we obtain some identities and congruences relating modular functionsj and η. We are hopeful that this representation can be extended to the whole groupF 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].