The Polarised $\Lambda$ production in QCD

The $Q^2$ evolution of polarised parton fragmentation functions is discussed using Altarelli-Parisi evolution equations. The first moments of both polarised quark and gluon fragmentation functions are shown to behave in a similar fashion at very high energies. This analysis is applicable to any hard processes involving production of polarised hadrons. The polarised $\Lambda$ hyperon production in $e^+~e^-$ annihilation where this can be realised is considered. We present a complete $\alpha_s(Q^2)$ corrections to the asymmetries discussed in the paper of Burkardt and Jaffe which demonstrates the extraction of various polarised fragmentation functions. To this order, these corrections are found to be scheme dependent similar to that of structure functions.