极Grassmannian的投射次Grassmannian
Projective Subgrassmannians of Polar Grassmannians
摘要：
在这个简短的说明中，完成了Cooperstein，Kasikova和Shult的一系列研究，我们考虑了有限秩n的一些极几何的k-格拉斯曼。我们对与射影m-空间的j-格拉斯曼同构的子空间进行了分类。在几乎所有的情况下，这些都是抛物线，也就是说，它们是极几何的旗帜的残基。只有当子空间同构于射影m-空间中的2-空间的格拉斯曼时，才会发生这种情况，我们对此进行了详细的描述。这个维特型结果意味着格拉斯曼的自同构几乎总是由底层极空间的自同构诱导的。
英文摘要：
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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