Abstract

A classification is given of models in which there are several Higgs $SU(2{)}_{L}$ doublets that form an irreducible multiplet of a non-Abelian symmetry ${G}_{\ensuremath{\Phi}}$, under which the quarks and leptons do not transform (thus giving minimal flavor changing for the fermions). It is found that different groups ${G}_{\ensuremath{\Phi}}$ and irreducible representations ${R}_{\ensuremath{\Phi}}$ of the Higgs fields under ${G}_{\ensuremath{\Phi}}$ lead to very distinctive spectra of the extra Higgs doublets, including different numbers of ``inert Higgs'' that could play the role of dark matter, different mass relations, and different patterns of $SU(2{)}_{L}$-breaking splittings within the Higgs doublets.

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