Generation Symmetry and E_6 Unification

Understand

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.