Luminescence spectroscopy is very sensitive to electron correlation in two-dimensional (2D) systems: intensity modulation clearly identifies hierarchies of fractional quantum Hall states. We report measurements that reveal that the interaction between 2D electrons and a photoexcited valence-band hole, which is of fundamental importance in determining the recombination spectrum, is enhanced in a low-density 2D electron system. As a result, the luminescence energy is insensitive to the electron ground state in this system and a distinct Fermi-edge singularity is observed at zero and low magnetic fields