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

2011/06/27 by Mark Pankov, Pankov, Mark
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO

paper · pdf · doi:10.48550/arxiv.1106.5435

openalex publication_date 2011/06/27 · arxiv created 2014/01/11 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Π be a polar space of type \textsfD_n. Denote by \mathcal G_δ(Π), δ∈ \+,-\ the associated half-spin Grassmannians and write Γ_δ(Π) for the corresponding half-spin Grassmann graphs. In the case when n≥ 4 is even, the apartments of \mathcal G_δ(Π) will be characterized as the images of isometric embeddings of the half-cube graph (1)/(2)H_n in Γ_δ(Π). As an application, we describe all isometric embeddings of Γ_δ(Π) in the half-spin Grassmann graphs associated to a polar space of type \textsfD_n' under the assumption that n≥ 6 is even.

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