Let V and V? be 2n-dimensional vector spaces over fields F and F?. Let also ?: V× V? F and ??: V?× V?? F? be non-degenerate symplectic forms. Denote by ? and ?? the associated (2n?1)-dimensional projective spaces. The sets of k-dimensional totally isotropic subspaces of ? and ?? will be denoted by $${\mathcal G}_{k}$$ and ${\mathcal G}'_{k}$, respectively. Apartments of the associated buildings intersect $${\mathcal G}_{k}$$ and $${\mathcal G}'_{k}$$ by so-called base subsets. We show that every mapping of $${\mathcal G}_{k}$$ to $${\mathcal G}'_{k}$$ sending base subsets to base subsets is induced by a symplectic embedding of ? to ??.