The long-standing problem of explaining the observed polarization of Lambda
hyperons, inclusively produced in the high-energy collisions of unpolarize
d hadrons, is tackled by considering spin- and k(perpendicular to)-dependen
t quark-fragmentation functions. The data on Lambda 's and <(<Lambda>)over
bar>'s produced in p-N processes are used to determine simple phenomenologi
cal expressions for these new "polarizing fragmentation functions," which d
escribe the experiments remarkably well.