  The optical orientation and alignment of excitons in semiconductor indirect
gap quantum dots have been studied theoretically. A special regime is analyzed
in which the energy of the hyperfine interaction of an electron with lattice
nuclei is small compared to the exchange splitting between bright and dark
excitonic levels, but is comparable to the anisotropic exchange splitting of
the radiative doublet. The dependencies of degrees of circular and linear
polarization on the external magnetic field under resonant excitation of
excitons by polarized light are calculated.
