Consider the $SU(3)$ part of the standard model. It appears that every fundamental particle in the standard model either lives in the trivial (leptons), the fundamental representation (quarks), or the antifundamental representation (antiquarks). Generalizing this idea, it appears that matter in the standard model does not live in higher irreducible representations of the gauge group $G$. Is there some a priori reason why this must be true? Moreover, if it isn't exactly true that this is satisfied in the standard model, correct me where I am wrong.