Successive symmetry breaking of a compact Lie group by a single irreducible multiplet of Higgs bosons

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Abstract
Using the {210}-dimensional Higgs representation of the SO(10) group as an example, we demonstrate the possibility of having a stable successive symmetry breaking (or phase transition) of a compact Lie group by a single irreducible multiplet of the Higgs boson (or order parameter). Such a symmetry breaking, which is stable under small fluctuations, was hitherto conjectured to be impossible by a weaker form of Michel’s conjecture. For example, one can use a single {210} to perform the stable, two-step symmetry breaking: SO(10)→SU(2)×SU(2)×SU(3)×U(1)× (D)→SU(2)×SU(2)×SU(3) ×U(1).