Lambda_b polarization in the Z boson decays

In the framework of the perturbative QCD and the diquark model of baryons we have obtained the fragmentation functions for heavy quark that split into polarized Lambda_b baryons. We predict the longitudinal polarization asymmetry for the prompt Lambda_b produced in electron-positron annihilation at the Z resonance and estimate the spin-1/2 and spin-3/2 beauty baryon production rate.