Abstract
The group ${E}_{6}$ for grand unification is combined with the generation symmetry group $SO(3{)}_{g}$. The coupling matrices in the Yukawa interaction are identified with the vacuum expectation values of scalar fields which are representations of the generation symmetry. These values determine the hierarchy of the fermions as well as their mixings and $CP$ violation. This generation mixing appears in conjunction with the mixing of the standard model fermions with the heavy fermions present in the lowest representation of ${E}_{6}$. A close connection between charged and neutral fermions is observed relating for instance the Cabibbo-Kobayashi-Maskawa (CKM) mixings with the mass splittings of the light neutrinos. Numerical fits with only a few parameters reproduce quantitatively all known fermion properties. The model predicts an inverted neutrino hierarchy and gives rather strict values for the light and heavy neutrino masses as well as for the $0\ensuremath{\nu}2\ensuremath{\beta}$ decay parameter. It also predicts that the masses of the two lightest of six ``right handed'' neutrinos lie in the low TeV region.
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