  The study of the pi^- p -> rho^0 n and pi^- p -> omega n amplitudes close and
below the vector meson production threshold (1.2< sqrt(s) <1.8 GeV) reveals a
rich dynamics arising from the presence of specific baryon resonances in this
energy range. The interference pattern of the e^+e^- decays of the rho^0 and
omega mesons produced in pi^- p reactions reflects directly this dynamics. We
discuss this interference pattern in the pi^- p -> e^+e^- n reaction as
function of the total center of mass energy sqrt(s). We emphasize the
importance of an experimental study of this reaction, which could be made with
the HADES detector and the available pion beam at GSI.
