A new family symmetry for image GUTs Original Research Article

We argue that the projective special linear group image, also known as image, has unique features which make it the most suitable discrete family symmetry for describing quark and lepton masses and mixing in the framework of image type unified models. In such models flavon fields in the sextet representation of image play a crucial role both in obtaining tri-bimaximal neutrino mixing as well as in generating the third family charged fermion Yukawa couplings. In preparation for physical applications, we derive the triplet representation of image in the basis image where image are the familiar triplet generators of image in the diagonal charged lepton basis where T is diagonal. We also derive an analogous basis for the real sextet representation and identify the vacuum alignments which lead to tri-bimaximal neutrino mixing and large third family charged fermion Yukawa couplings.