  We report on the theoretical photoluminescence spectrum of the interacting
two-dimensional electron gas at filling factor one (\nu=1). We considered a
model similar to the one adopted to study the X-ray spectra of metals and
solved it analytically using the bosonization method previously developed for
the two-dimensional electron gas at \nu=1. We calculated the emission spectra
of the right and the left circularly polarized radiations for the situations
where the distance between the two-dimensional electron gas and the valence
band hole are smaller and greater than the magnetic length. For the former, we
showed that the polarized photoluminescence spectra can be understood as the
recombination of the so-called excitonic state with the valence band hole
whereas, for the latter, the observed emission spectra can be related to the
recombination of a state formed by a spin down electron bound to n spin waves.
This state seems to be a good description for the quantum Hall skyrmion.
