  A sequence of photoluminescence spectroscopy based methods are used to
rigorously identify and study all the main spectral features (more than thirty
emission lines) of site controlled InGaAs/AlGaAs quantum dots (QDs) grown along
[111]B in inverted tetrahedral pyramids. The studied QDs reveal signatures of
one confined electron level, one heavy-hole-like level and one light-hole-like
level. The various heavy-light-hole hybrid exciton complexes formed in these
QDs are studied by polarization resolved spectroscopy, excitation power
dependence, crystal temperature dependence and temporal single photon
correlation measurements. The presented approach, which only requires a minimal
theoretical input, enables strict spectral identification of the fine structure
patterns including weak and spectrally overlapping emission lines. Furthermore,
it allows the involved electron-hole and hole-hole exchange interaction
energies to be deduced from measurements. Intricate fine structure patterns are
qualitatively understood by group theory and shown to be very sensitive to the
exact symmetry of the QD. Emission patterns influenced by hole-hole exchange
interactions are found to be particularly useful for identifying QDs with high
$C_{3v}$ symmetry and for probing symmetry breaking.
