Pseudo-embeddings of the (point, k-spaces)-geometry of PG(n, 2) and projective embeddings of DW(2n-1, 2)

Abstract

We classify all homogeneous pseudo-embeddings of the point-line geometry defined by the points and k-dimensional subspaces of PG(n, 2), and use this to study the local structure of homogeneous full projective embeddings of the dual polar space DW(2n-1, 2). Our investigation allows us to distinguish n possible types for such homogeneous embeddings. For each of these n types, we construct a homogeneous full projective embedding of DW(2n - 1, 2)