Base subsets of polar Grassmannians

Mark Pankov

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arXiv · math/0611527

Base subsets of polar Grassmannians

Mark Pankov

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Abstract

Let $Δ$ be a thick building of type $\textsf{X}_{n}=\textsf{C}_{n},\textsf{D}_{n}$. 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 $\textsf{X}_{n,k}$. 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 $n\ne 4$ or $k\ne 1$.

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BibTeX RIS

Mark Pankov. 2006-12-06. Base subsets of polar Grassmannians. https://arxiv.org/abs/math/0611527

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