Borcherds' proof of the Conway-Norton conjecture

Details Borcherds' proof of the Conway-Norton conjecture Borcherds' proof of the Conway-Norton conjecture

2009-03-25

arxiv.org/abs/0903.4456v1

Mathematics

Representation Theory

First presented at Moonshine - the first quarter century and beyond.A Workshop on the Moonshine Conjectures and Vertex Algebra

Scientific paper

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.

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