Bulletin of the Belgian Mathematical Society - Simon Stevin

Characterization of apartments in polar Grassmannians

Mark Pankov

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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.

Article information

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

Dates
First available in Project Euclid: 24 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1337864278

Digital Object Identifier
doi:10.36045/bbms/1337864278

Mathematical Reviews number (MathSciNet)
MR2977237

Zentralblatt MATH identifier
1247.51007

Subjects
Primary: 51A50: Polar geometry, symplectic spaces, orthogonal spaces 51E24: Buildings and the geometry of diagrams

Keywords
polar space polar Grassmannian apartment

Citation

Pankov, Mark. Characterization of apartments in polar Grassmannians. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 345--366. doi:10.36045/bbms/1337864278. https://projecteuclid.org/euclid.bbms/1337864278


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