  We study the splitting between the right-hand and left-hand circularly
polarized luminescence lines in a quantum dot under relatively weak confinement
regime and resonant high-power excitation. When the dot is populated with an
even number of electron-hole pairs (biexciton and higher excitations), the
splitting measures basically the Zeeman energy. However, in the odd number of
pairs case, we have, in addition to the Zeeman and Overhauser shifts, a
contribution to the splitting coming from Coulomb interactions. This
contribution is of the order of a few meV, and shows distinct signatures of
shell-filling in the quantum dot.
