Conformal E-infinity theory, exceptional Lie groups and the elementary particle content of the standard model

We begin with Klein's original modular space Γ(7) for whichD=DimΓ(7)=|SL(2,7)=336.Subsequent compactificationD=336⇒Dc=D+16k≃339and conformal transformation leads toDc≅339⇒Dcom=(Dc)(1/ϕ)≃548.We observe that this result is identical to summing over all dimensions of the exceptional Lie symmetry groups hierarchy G2, F4, E6, E7 and E8 and adding A1, A2 and the standard model SM gauge boson to the result. That means∑exDim Lie=|A1|+|A2|+|G2|+|F4|+|E6|+|E7|+|E8|=3+8+14+52+78+133+248=536and therefore∑exDim Lie+|SM|=536+12=548=Dcom.This result is a neat confirmation of the basic group theoretical assumptions of the standard model, namely ∣SU(3) SU(2) U(1)∣ = 12 as well as our previous expectation number of the elementary particles in an extended standard model:N(S)=(548+4k0)/8=α¯0/2=137+k0≃69particles.