The generating rank of the unitary and symplectic Grassmannians

الأصل · EN

We prove that the Grassmannian of totally isotropic k-spaces of the polar space associated to the unitary group SU₂ₙ(F) (n∈ N) has generating rank 2n k when F≠ F₄. We also reprove the main result of Blok [Blok2007], namely that the Grassmannian of totally isotropic k-spaces associated to the symplectic group Sp₂ₙ(F) has generating rank 2n k-2n k-2, when Char(F)≠ 2.