  We study $SU(n)$ symmetry breaking by rank three and rank two antisymmetric
tensor fields. Using tensor analysis, we derive branching rules for the adjoint
and antisymmetric tensor representations, and explain why for general $SU(n)$
one finds the same $U(1)$ generator mismatch that we noted earlier in special
cases. We then compute the masses of the various scalar fields in the branching
expansion, in terms of parameters of the general renormalizable potential for
the antisymmetric tensor fields.
