Symmetric versus antisymmetric mass matrices in grand unified theories

We point out some interesting consequences of antisymmetric fermionic mass terms in grand unified theories, which follow from the symmetry properties of the Yukawa-type fermion-Higgs interactions. In SU(5), we show that an antisymmetric mass matrix M(u) in the up-quark sector arises when the Higgs 5 is replaced by 45. IOn SO(10), all the fermion sectors are characterized by such mass matrices if the neutrinos are required not to pick up the ordinary fermionic mass scale. In the recently proposed vertical-horizontal symmetric SU(5) × SU(5) scheme, a fully antisymmetric M(u) is naturally accompanied by exactly five zeroth-order massless neutrinos.