  We discuss the relation between the ratio of the proton-deuteron (pd)
Drell-Yan cross section to the proton-proton (pp) one \Delta_{(T)}
\sigma_{pd}/2 \Delta_{(T)} \sigma_{pp} and the flavor asymmetry in polarized
light-antiquark distributions. Using a recent formalism of the polarized pd
Drell-Yan process, we show that the difference between the pp and pd cross
sections is valuable for finding not only the flavor asymmetry in
longitudinally polarized antiquark distributions but also the one in
transversity distributions. It is especially important that we point out the
possibility of measuring the flavor asymmetry in the transversity distributions
because it cannot be found in W production processes and inclusive lepton
scattering due to the chiral-odd property.
