The infinitesimal cone of a totally positive semigroup

Rietsch, Konstanze

doi:10.1090/S0002-9939-97-03931-2

The infinitesimal cone of a totally positive semigroup
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Proc. Amer. Math. Soc. 125 (1997), 2565-2570 Request permission

Abstract:

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

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