Families from USp(32)

The same trick to descent to three generations can be done starting from the 495 of Sp(32). We are on it, as usual, in physicsforums


As noted there, we still lack of a variant showing the L-R chirality of the SM.  I wonder if we could use some exotic models from E6 or E8 for this. Particularly I am thinking on some innovative usage of the 27-dim irrep of E6, perhaps decoloring it so that all the three generations can be put where colour usually is. It could be interesting for instance if it goes to 24+3 purging the +4/3 quarks.

Models based on non commutative geometry with octonions or Jordan Algebras could be interesting to look at, for this task. Perhaps https://arxiv.org/abs/1604.01247 or something with hints of composite higgses.

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