The infinitesimal cone of a totally positive semigroup

Source abstract

Given a complex reductive linear algebraic group split over R \mathbb {R} with a fixed pinning, it is shown that all elements of the Lie algebra g \mathfrak {g} infinitesimal to the totally positive subsemigroup G ≥ 0 G_{\ge 0} of G G lie in the totally positive cone g ≥ 0 ⊂ g \mathfrak {g}_{\ge 0}\subset \mathfrak {g} .