Projective Subgrassmannians of Polar Grassmannians

2010/10/01 by Blok, Rieuwert J., Cooperstein, Bruce N.
#51A50 (Primary) #51E24 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1010.0199

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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