Witt-Type Theorems for Grassmannians and Lie Incidence Geometries

Abstract

Abstract For a subset of a Lie incidence geometry two intrinsic notions of independence are introduced. Also defined is the notion of a parabolic subspace. A classification is achieved for certain independent subgraphs of the point collinearity graph of the Lie incidence geometries An,k , Bn,n , Dn,n . As a corollary it is proved that certain subspaces of these geometries are parabolic and transitivity results are obtained.