  We study the theory of itinerant-hole photoluminescence of two-dimensional
electron systems in the regime of the magnetically induced Wigner crystal. We
show that the exciton recombination transition develops structure related to
the presence of the Wigner crystal. The form of this structure depends strongly
on the separation $d$ between the photo-excited hole and the plane of the
two-dimensional electron gas. When $d$ is small compared to the magnetic
length, additional peaks appear in the spectrum due to the recombination of
exciton states with wavevectors equal to the reciprocal lattice vectors of the
crystal. For $d$ larger than the magnetic length, the exciton becomes strongly
confined to an interstitial site of the lattice, and the structure in the
spectrum reflects the short-range correlations of the Wigner crystal. We derive
expressions for the energies and the radiative lifetimes of the states
contributing to photoluminescence, and discuss how the results of our analysis
compare with experimental observations.
