Compact analytic expressions have been obtained for the first order
perturbative QCD corrections to the inclusive spectra of the leptons
in the semileptonic decays of polarised heavy quarks.
Charmed and beautiful $\Lambda$ baryons from $Z^0$ decays can be
viewed as sources of highly polarised charm and bottom quarks.
Charged leptons and neutrinos from $\Lambda_b$ and $\Lambda_c$ decays
can be used in the polarisation studies for the corresponding heavy
quarks. Thus our results are applicable for the b quark polarisation
measurements at LEP.
Short lifetime enables polarisation studies for the top quark. The
angular-energy spectra of the charged leptons are particularly useful
in this respect whereas the distributions of the neutrinos are
sensitive to deviations from the V-A structure of the charged weak
current in the decay.