Base subsets of polar Grassmannians

2006/11/17 by Mark Pankov, Pankov, Mark
Computer Science · Mathematics · #14M15 #51M35 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.math/0611527

openalex publication_date 2006/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Δ be a thick building of type \textsfX_n=\textsfC_n,\textsfD_n. Let also \mathcal G_k be the Grassmannian of k-dimensional singular subspaces of the associated polar space Π (of rank n). We write \mathfrak G_k for the corresponding shadow space of type \textsfX_n,k. Every bijective transformation of \mathcal G_k sending base subsets to base subsets (the shadows of apartments) is a collineation of \mathfrak G_k, and it is induced by a collineation of Π if n≠ 4 or k≠ 1.

Related

• Characterization of apartments in polar Grassmannians
• Metric characterization of apartments in dual polar spaces
• Transformations of polar Grassmannians preserving certain intersecting relations
• Transformations of Grassman Spaces
• Isometric embeddings of polar Grassmannians and metric characterizations of their apartments