Total positivity in partial flag manifolds

Abstract

The projective space of R n \mathbf {R}^{n} has a natural open subset: the set of lines spanned by vectors with all coordinates > 0 >0 . Such a subset can be defined more generally for any partial flag manifold of a split semisimple real algebraic group. The main result of the paper is that this subset can be defined by algebraic equalities and inequalities.