  We study the production of transversely polarized Lambda hyperons in
high-energy collisions of protons with large nuclei. The large gluon density of
the target at saturation provides an intrinsic semi-hard scale which should
naturally allow for a weak-coupling QCD description of the process in terms of
a convolution of the quark distribution of the proton with the elementary
quark-nucleus scattering cross section (resummed to all twists) and a
fragmentation function. In this case of transversely polarized Lambda
production we employ a so-called polarizing fragmentation function, which is an
odd function of the transverse momentum of the Lambda relative to the
fragmenting quark. Due to this k_t-odd nature, the resulting Lambda
polarization is essentially proportional to the derivative of the quark-nucleus
cross section with respect to transverse momentum, which peaks near the
saturation momentum scale. Such processes might therefore provide generic
signatures for high parton density effects and for the approach to the
``black-body'' (unitarity) limit of hadronic scattering.
