Group-theoretic evidence for SO(10) grand unification

The hypercharges of the fermions are not uniquely determined in SO(10) grand unification, but rather depend upon which linear combination of the two U(1) subgroups of SO(10)⊃SU(3)×SU(2)×U(1)×U(1) remains unbroken. We show that, in general, a given hypercharge assignment can be obtained only with very high-dimensional Higgs representations. The observation that the standard model is obtained with low-dimensional Higgs representations can therefore be regarded as further evidence for SO(10) grand unification. This evidence is independent of the fact that SO(10)⊃ SU(5).