  We study indirect exchange interaction between magnetic impurities in the
(001) CdTe/HgTe/CdTe symmetric quantum well. We consider low temperatures and
the case of the chemical potential placed in the energy gap of the 2D
quasiparticle spectrum. We find that the indirect exchange interaction is
suppressed exponentially with the distance between magnetic impurities. The
presence of inversion asymmetry results in oscillations of the indirect
exchange interaction with the distance and generates additional terms which are
non-invariant under rotations in the (001) plane. The indirect exchange
interaction matrix has complicated structure with some terms proportional to
the sign of the energy gap.
