On the generation of dual polar spaces of unitary type over finite fields (Q1372623)

Let \(U = U_{2n}(q^2)\) denote the \(2n\)-dimensional unitary vector space over a finite field of order \(q^2\). The dual polar space \(D = DU_{2n}(q^2)\) has as its points the isotropic subspaces of \(U\) of maximal dimension \(n\), and as its lines the \((n-1)\)-dimensional isotropic subspaces of \(U\); incidence is given by (reverse) inclusion. Main theorem. The minimal number of points that generate \(D\) is \(2n \choose n\).