## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

### Characterization of apartments in polar Grassmannians

#### 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