Borcherds' proof of the Conway-Norton conjecture
Representation Theory
2009-03-27 v1 Group Theory
Abstract
We give a summary of R. Borcherds' solution (with some modifications) to the following part of the Conway-Norton conjectures: Given the Monster simple group and Frenkel-Lepowsky-Meurman's moonshine module for the group, prove the equality between the graded characters of the elements of the Monster group acting on the module (i.e., the McKay-Thompson series) and the modular functions provided by Conway and Norton. The equality is established using the homology of a certain subalgebra of the monster Lie algebra, and the Euler-Poincare identity.
Keywords
Cite
@article{arxiv.0903.4456,
title = {Borcherds' proof of the Conway-Norton conjecture},
author = {Elizabeth Jurisich},
journal= {arXiv preprint arXiv:0903.4456},
year = {2009}
}
Comments
First presented at Moonshine - the first quarter century and beyond.A Workshop on the Moonshine Conjectures and Vertex Algebras ICMS, 5 - 13 July 2004