## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Characterization of apartments in polar Grassmannians

Mark Pankov

#### 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

https://projecteuclid.org/euclid.bbms/1337864278

Digital Object Identifier
doi:10.36045/bbms/1337864278

Mathematical Reviews number (MathSciNet)
MR2977237

Zentralblatt MATH identifier
1247.51007

#### 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