Fermion mass relations and the structure of the light Higgs in a supersymmetric SO(10) theory

Neutrino and charged fermion masses provide important constraints on grand unified theories. We illustrate this by focusing on a renormalizable, supersymmetric SO(10) theory proposed long ago, that recently attracted great interest in view of its minimality. We show how the nature of the light Higgs, which depends on the GUT scale fields, gets reflected on the precise predictions for fermion masses and mixings. We exemplify this on the case of dominant type II see-saw, which gets severely constrained and is likely to fail.