Fermion masses inSO(10)with a single adjoint Higgs field

It has recently been shown how to break $\mathrm{SO}\left(10\right)\mathrm{}$ down to the standard model in a realistic way with only one adjoint Higgs field. The expectation value of this adjoint must point in the $B-L$ direction. This has consequences for the possible form of the quark and lepton mass matrices. These consequences are explored in this paper, and it is found that one is naturally led to consider a particular form for the masses of the heavier generations. This form implies typically that there should be large (nearly maximal) mixing of the $\mu$ and $\tau$ neutrinos. An explanation that does not involve large $\tan \beta$ also emerges for the fact that $b$ and $\tau$ are light compared to the top quark.