  In phenomenological studies of low-energy supersymmetry, running gaugino
masses are often taken to be equal near the scale of apparent gauge coupling
unification. However, many known mechanisms can avoid this universality, even
in models with unified gauge interactions. One example is an F-term vacuum
expectation value that is a singlet under the Standard Model gauge group but
transforms non-trivially in the symmetric product of two adjoint
representations of a group that contains the Standard Model gauge group. Here,
I compute the ratios of gaugino masses that follow from F-terms in non-singlet
representations of SO(10) and E_6 and their sub-groups, extending well-known
results for SU(5). The SO(10) results correct some long-standing errors in the
literature.
