Projective Subgrassmannians of Polar Grassmannians
Group Theory
2010-10-04 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1010.0199,
title = {Projective Subgrassmannians of Polar Grassmannians},
author = {Rieuwert J. Blok and Bruce N. Cooperstein},
journal= {arXiv preprint arXiv:1010.0199},
year = {2010}
}