Convex functions on symmetric spaces, side lengths of polygons and stability inequalities for weighted configurations at infinity

Details Convex functions on symmetric spaces, side lengths of polygons and stability inequalities for weighted configurations at infinity Convex functions on symmetric spaces, side lengths of polygons and stability inequalities for weighted configurations at infinity

2003-11-26

arxiv.org/abs/math/0311486v3

Mathematics

Differential Geometry

Scientific paper

In a symmetric space of noncompact type X = G/K oriented geodesic segments correspond to points in the Euclidean Weyl chamber. We can hence assign vector-valued side-lengths to segments. Our main result is a system of homogeneous linear inequalities describing the restrictions on the side -lengths of closed polygons. The inequalities are based on the mod 2 Schubert calculus in the real Grassmannians G/P for maximal parabolic subgroups P.

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