Characterization of apartments in polar Grassmannians
type: Item
instance of: scholarly article
title: Characterization of apartments in polar Grassmannians
zbMATH Open document ID: 1247.51007
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2012-06-28T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.2555
full work available at URL: https://projecteuclid.org/euclid.bbms/1337864278
review text: 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.
reviewed by: Rolf Riesinger
Mathematics Subject Classification ID: 51A50
Mathematics Subject Classification ID: 51E24
zbMATH DE Number: 6050944
zbMATH Keywords: polar space
zbMATH Keywords: polar Grassmannian
zbMATH Keywords: apartment
author: Mark Pankov
MaRDI profile type: Publication
arXiv ID: 1109.2555
description: scientific article; zbMATH DE number 6050944