QCD corrections to the longitudinally polarized Drell-Yan process

In this paper we calculate the O($\alpha_s$) corrections to the $x_F$- and $y$-distributions of lepton pairs produced in collisions of longitudinally polarized hadrons. The numerical importance of these corrections is studied and consequences for the extraction of the polarized sea quark distributions from a measurement of the longitudinally polarized Drell-Yan cross section are discussed.