The PF thread
discussing Lisi's work (and the E8 talk by Kostant
) contains a link to Baez's
page on some interesting remarks by McKay
, alluded to by Gannon
). McKay says:
There is a remarkable connection between the three groups: Monster, 2.Baby Monster and 3.F24, and the graphs for E8, E7, and E6 respectively ... We may [alternatively] work with the folded Dynkin graphs of type E8, F4, G2 and collapse the centre. By moonshine, this means that each node of these extended graphs can be labelled by a modular function given by the moonshine correspondence, with the elliptic modular function j(z) corresponding to the identity of the Monster and so to the affine node of the E8 Dynkin graph. There is a similar interpretation for the other nodes. Adjacency is not understood but there should be a mechanism for obtaining the neighbours of a moonshine modular function occurring here.