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We study the theory of intrinsic photoluminescence of two-dimensionalelectron systems in the vicinity of the $\nu=1$ quantum Hall state. We focuspredominantly on the recombination of a band of initial ``excitonic states''that are the low-lying energy states of our model at $\nu=1$. It is shown thatthe recombination of excitonic states can account for recent observations ofthe polarization-resolved spectra of a high-mobility GaAs quantum well. Theasymmetric broadening of the spectral line in the $\sigma_-$ polarization isexplained to be the result of the ``shake-up'' of spin-waves upon radiativerecombination of excitonic states. We derive line shapes for the recombinationof excitonic states in the presence of long-range disorder that comparefavourably with the experimental observations. We also discuss the stabilitiesand recombination spectra of other (``charged'') initial states of our model.An additional high-energy line observed in experiment is shown to be consistentwith the recombination of a positively-charged state. The recombinationspectrum of a negatively-charged initial state, predicted by our model but notobserved in the present experiments, is shown to provide a direct measure ofthe formation energy of the smallest ``charged spin-texture'' of the $\nu=1$state.Comment: 23 pages, 7 postscript figures included. Revtex with epsf.tex and  multicol.sty. The revised version contains slightly improved numerical  results and a few additional discussions of the result

Theory of photoluminescence of the ν=1 quantum Hall state:Excitons, spin waves, and spin textures