Projective Subgrassmannians of Polar Grassmannians
Blok, Rieuwert J. ; Cooperstein, Bruce N.
Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, p. 675-691 / Harvested from Project Euclid
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In this short note, completing a sequence of studies, 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.
Publié le : 2010-08-15
Classification:  Grassmannian,  polar geometry,  embeddings,  51A50,  51E24 
@article{1290608194,
     author = {Blok, Rieuwert J. and Cooperstein, Bruce N.},
     title = {Projective Subgrassmannians of Polar Grassmannians},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {17},
     number = {1},
     year = {2010},
     pages = { 675-691},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1290608194}
}

Blok, Rieuwert J.; Cooperstein, Bruce N. Projective Subgrassmannians of Polar Grassmannians. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp.  675-691. http://gdmltest.u-ga.fr/item/1290608194/