and that the fermions form three families, each consisting of the representations: , , and . The L includes a hypothetical right-handed neutrino, which may account for observed neutrino masses (see neutrino oscillations), and a similar sterile "flavon."
Note that there are two Majorana neutrinos per generation (which is consistent with neutrino oscillations). Also, each generation has a pair of triplets and , and doublets and , which decouple at the GUT breaking scale due to the couplings
and
.
Note that calling representations things like and (8,1,1) is purely a physicist's convention, not a mathematician's, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, but it is standard among GUT theorists.
Trinification is a of E6, whose matter representation 27 has exactly the same representation and unifies the fields. E6 adds 54 gauge bosons, 30 it shares with SO(10), the other 24 to complete its .
References[]
^De Rujula, A.; Georgi, H.; Glashow, S. L. (1984). "Trinification of all elementary particle forces". In Kang, K.; Fried, H.; Frampton, F. (eds.). Fifth Workshop on Grand Unification. Singapore: World Scientific.