The classification of flats in \(\text{PG}(\mathbf{9,2})\) which are external to the Grassmannian \({\mathcal G}_{\mathbf{1,4,2}}\)
In this paper the authors are concerned with those flats in the projective space \(\text{PG}(9, 2)= \mathbb{P}(V(5, 2)\wedge V(5, 2))\), which are external to the Grassmannian \(\mathcal H\) arising from the 155 lines of the projective space \(\text{PG}(4, 2)= \mathbb{P}(V(5, 2))\). On the basis of three unpublished papers, which are available via the internet, a complete classification of all external \(k\)-flats is given. Apart from the trivial class of \(0\)-flats there are nine further classes. For \(k= 1,3,4\) there are two classes and in the case \(k= 2\) there are three different types. In any case each class is an orbit under the induced action of the linear group \(\text{GL}(5, 2)\) on the projective space \(\text{PG}(9,2)\).
scientific article; zbMATH DE number 2139254