Combinatorial Theory

We classify the convex subspaces of all hexagonic Lie incidence geometries (among which all long root geometries of spherical Tits-buildings). We perform a similar classification for most other Lie incidence geometries of spherical Tits-buildings, in particular for all projective and polar Grassmannians, and for exceptional Grassmannians of diameter at most 3.

Mathematics Subject Classifications: 51E24

Keywords: Buildings, parapolar spaces, long root geometries, hexagonal Lie incidence geometries