I don't have access to Georgi's and Wilcheck's work, if somebody has some good links to an overview of the su(5), so(10), and e6 GUTS that would be awesome. Anyways, there's something I really don't get, lets take su(5) for example, su(5) has the root system [tex]A_4[/tex] now there is 4(4+2) = 24 generators of the lie algebra. Now I know they didn't use all 24 of the generators because it would mean that there were 24 gauge bosons, not including the Higgs. So I heard they used a diagonal representation of su(5). Something like [su(3)0] [0 su(2)] Does that entail just using the Cartan subalgebra or what? What did they do?