Division Algebras, Lie Algebras, Lie Groups and Spinors
Let me stress that this is a purely mathematical result. With respect to the Lie group
SU(3) generated from the Lie algebra above, W transforms as the direct sum of an
SU(3) singlet, triplet, antisinglet, and antitriplet. The corresponding SU(3) charges
AND U(1) charges are exactly those we encounter in the standard model of quarks
and leptons. The standard model also has an SU(2) internal symmetry. That and
much more are covered in the pdf (see bottom of Contents), and especially in the book.
Personally I find this mathematical result and physical correspondence totally cool.
Cheers.