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arXiv · 1010.0199

Projective Subgrassmannians of Polar Grassmannians

Rieuwert J. Blok·Bruce N. Cooperstein
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Abstract

In this short note, completing a sequence of studies by Cooperstein, Kasikova and Shult, we consider the k-Grassmannians of a number of polar geometries of finite rank n. We classify those subspaces that are isomorphic to the j-Grassmannian of a projective m-space. In almost all cases, these are parabolic, that is, they are the residues of a flag of the polar geometry. Exceptions only occur when the subspace is isomorphic to the Grassmannian of 2-spaces in a projective m-space and we describe these in some detail. This Witt-type result implies that automorphisms of the Grassmannian are almost always induced by automorphisms of the underlying polar space.

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Rieuwert J. Blok, Bruce N. Cooperstein. 2010-10-01. Projective Subgrassmannians of Polar Grassmannians. https://arxiv.org/abs/1010.0199

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