  We present an experimental and theoretical study of the polarized
photoluminescence spectrum of single semiconductor quantum dots in various
charge states. We compare our high resolution polarization sensitive spectral
measurements with a new many-carrier theoretical model, which was developed for
this purpose. The model considers both the isotropic and anisotropic exchange
interactions between all participating electron-hole pairs. With this addition,
we calculate both the energies and polarizations of all optical transitions
between collective, quantum dot confined charge carrier states. We succeed in
identifying most of the measured spectral lines. In particular, the lines
resulting from singly-, doubly- and triply- negatively charged excitons and
biexcitons. We demonstrate that lines emanating from evenly charged states are
linearly polarized. Their polarization direction does not necessarily coincide
with the traditional crystallographic direction. It depends on the shells of
the single carriers, which participate in the recombination process.
