  We present a comprehensive theory of the circularly polarized luminescence
and its dependence on strain in spin-polarized Si and Ge. Symmetries of
wavefunctions and interactions are used to derive concise ratios between
intensities of the right and left circularly polarized luminescence for each of
the dominant phonon-assisted optical transitions. These ratios are then used to
explain the circular polarization degrees of the luminescence peaks in the
spectra of biaxially-strained Si and Ge, and of relaxed
${\rm{Si}}_{1-x}{\rm{Ge}}_{x}$ alloys. The spectra are numerically calculated
by a combination of an empirical pseudopotential method, an adiabatic
bond-charge model and a rigid-ion model.
