Gauge group representations in the Standard Model?

Question

Why is it that all the fields in the Standard Model form either the trivial, fundamental, or adjoint representation of the gauge groups? It obviously makes sense to me why they should be irreducible representations, but why always these three? Does this suggest anything about the GUT or SUSY group these particles might form a representation of?

Answer 1

I don't think you can ask why necessarily. That's just how is works out. Folks are guessing that GUT might be able to combine everything into a single simple group, although it's not obvious how that would work without allowing proton decay and stuff that we don't observe.