  We investigate the origin of emission lines apparent in the low-temperature
photoluminescence spectra of $n$-doped WS$_2$ monolayer embedded in hexagonal
BN layers using external magnetic fields and first-principles calculations.
Apart from the neutral A exciton line, all observed emission lines are related
to the negatively charged excitons. Consequently, we identify emissions due to
both the bright (singlet and triplet) and dark (spin- and momentum-forbidden)
negative trions as well as the phonon replicas of the latter optically-inactive
complexes. The semi-dark trions and negative biexcitons are distinguished.
Based on their experimentally extracted and theoretically calculated
$g$-factors, we identify three distinct families of emissions due to exciton
complexes in WS$_2$: bright, intravalley and intervalley dark. The $g$-factors
of the spin-split subbands in both the conduction and valence bands are also
determined.
