With the idea of Dubois-Violette about using a Jordan Algebra to build three generations of the standard model I had had the hope of finding our lost -4/3 quarks as part of the content of a 27 + 27 representation of E6. Asuming this was to be interpreted as the “decoloured” part of the standard model so that colour is actually generation. Indeed this representation allows for branching with three (six, counting L and R) charged leptons, but a preliminary exploration of such representations only finds three or four variants of the extra content:
- 2 states with -4/3, three with +1/3, one with +5/3
- (and the opposite of that one)
- -5/3, -2/3, -1/3, +1/3, +2/3, +5/3
- -5/3, -4/3, -1/3, +1/3, +4/3, +5/3
On other hand, DV did not used 27 ìn this way, but he used it not only decouloring the quarks but also “de-weaking” the standard model, so that it needed to use one 27 for the “up quarks” and another 27 for the “down quarks”. But this version doesnt fit either with the sBootstrap extra content, as we only have tree +4/3 quarks, without any weak isospin partner. So the precise DV image should be a 27 + 24, plus antiparticles.