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

Kapovich, Misha; Leeb, Bernhard; Millson, John J.

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

Authors

Kapovich, Misha

Leeb, Bernhard

Millson, John J.

Description

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.