We report on the theoretical photoluminescence spectrum of an 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 is 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.7124