Base subsets of polar Grassmannians

Details Base subsets of polar Grassmannians Base subsets of polar Grassmannians

2006-11-17

arxiv.org/abs/math/0611527v3

Mathematics

Combinatorics

Scientific paper

Let $\Delta$ 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 $\Pi$ (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 $\Pi$ if $n\ne 4$ or $k\ne 1$.

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