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.
Citation
Mark Pankov. "Characterization of apartments in polar Grassmannians." Bull. Belg. Math. Soc. Simon Stevin 19 (2) 345 - 366, march 2012. https://doi.org/10.36045/bbms/1337864278
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