Characterization of apartments in polar Grassmannians
Let \(\Pi\) be a polar space of rank \(n\geq\,3\) and let \(\Gamma_k(\Pi)\) be the Grassmann graph formed by the \(k\)-dimensional subspaces of \(\Pi\). The author investigates the embeddings of the polar Johnson graph \(PJ(l,m)\) in \(\Gamma_k(\Pi)\) such that \(m\leq\,k\leq\,n-2\) and \(l-m\leq\,n-k\). In the case with \(l-m=n-k\) the author gets a characterization of apartments in parabolic subspaces of the associated Grassmann space. As application the author shows that parabolic subspaces can be characterized as convex subspaces isomorphic to polar Grassmann spaces.
scientific article; zbMATH DE number 6050944