Isometric embeddings of half-cube graphs in half-spin Grassmannians

Mark Pankov¹

¹University of Warmia and Mazury

The electronic journal of combinatorics, Tome 21 (2014) no. 4

Résumé

Let $\Pi$ be a polar space of type $\textsf{D}_{n}$. Denote by ${\mathcal G}_{\delta}(\Pi)$, $\delta\in \{+,-\}$ the associated half-spin Grassmannians and write $\Gamma_{\delta}(\Pi)$ for the corresponding half-spin Grassmann graphs. In the case when $n\ge 4$ is even, the apartments of ${\mathcal G}_{\delta}(\Pi)$ will be characterized as the images of isometric embeddings of the half-cube graph $\frac{1}{2}H_n$ in $\Gamma_{\delta}(\Pi)$. As an application, we describe all isometric embeddings of $\Gamma_{\delta}(\Pi)$ in the half-spin Grassmann graphs associated to a polar space of type $\textsf{D}_{n'}$ under the assumption that $n\ge 6$ is even.

Détail

DOI : 10.37236/4107

Classification : 51A50, 51E24, 51A45
Mots-clés : half-cube graph, half-spin Grassmann graph