Characterization of apartments in polar Grassmannians

2011/09/12 by Pankov, Mark
#51A50 #51E24 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.2555

Abstract

Buildings of types \textsfC_n and \textsfD_n are defined by rank n polar spaces. The associated building Grassmannians are polar and half-spin Grassmannians. Apartments in dual polar spaces and half-spin Grassmannians were characterized in \citeCKS. We characterize apartments in all polar Grassmannians consisting of non-maximal singular subspaces. This characterization is a partial case of more general results concerning embeddings of polar Johnson graphs in polar Grassmann graphs.

Related

• Metric characterization of apartments in dual polar spaces
• Isometric embeddings of polar Grassmannians and metric characterizations of their apartments
• Base subsets of polar Grassmannians
• Grassmannians of classical buildings
• Transformations of Grassman Spaces