Totally nonnegative and oscillatory elements in semisimple groups
  We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F.R.Gantmacher, M.G.Krein, A.Whitney, C.Loewner, M.Gasca, and J.M.Pena to the case of an arbitrary complex semisimple Lie group. 
Sergey Fomin and Andrei Zelevinsky