Characterization of apartments in polar Grassmannians

Mark Pankov
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 19, Number 2 (2012), 345-366.

Abstract

Buildings of types $\textsf{C}_n$ and $\textsf{D}_n$ 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 [4]. 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.

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Primary Subjects: 51A50, 51E24