  Recent e+e- annihilation experiments show a striking spin alignment of vector
mesons produced in the fragmentation of a polarized quark.We show that these
data imply a simple relation between the polarization of the anti-quark, which
is produced in the fragmentation process to combine with the fragmenting quark
to form the meson, and that of the fragmenting quark. After having obtained a
good fit to the e+e- data, we extend the calculations to lepton-nucleon and
nucleon-nucleon collisions with polarized beams. We also discuss the relation
between the spin alignment of vector meson in unpolarized hadron-hadron
collisions and the single-spin left-right asymmetry. We make predictions for
the polarization of the vector mesons in these reactions which can be checked
by future experiments.
