  The dielectric environment of atomically-thin monolayer (ML) of
semiconducting transition metal dichalcogenides affects both the electronic
band gap and the excitonic binding energy in the ML. We investigate the effect
of the environment on the in-plane magnetic field brightening of neutral and
charged dark exciton emissions in the WSe$_2$ ML. The monolayers placed in
three dielectric environments are studied, in particular, the ML encapsulated
in hexagonal BN (hBN) flakes, the ML deposited on a hBN layer, and the ML
embedded between the hBN flake and SiO$_2$/Si substrate. We observe that the
brightening rates of the neutral and charged dark excitons depend on the
dielectric environment, which may be related to the variation of the level of
carrier concentration in the ML. Moreover, the surrounding media, characterized
by different dielectric constants, influences weakly the relative energies of
the neutral and charged dark excitons in reference to the bright ones.
