Symplectic subspaces of symplectic Grassmannians

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Abstract

Let V be a non-degenerate symplectic space of dimension 2n over the field F and for a natural number l<n denote by Cl(V) the incidence geometry whose points are the totally isotropic l-dimensional subspaces of V. Two points U,W of Cl(V) will be collinear when WU and dim(UW)=l1 and then the line on U and W will consist of all the l-dimensional subspaces of U+W which contain UW. The isomorphism type of this geometry is denoted by Cn,l(F). When char(F)2 we classify subspaces S of Cl(F) where SCm,k(F).

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