Universal equations for maximal isotropic Grassmannians

The isotropic Grassmannian parametrizes isotropic subspaces of a vector space equipped with a quadratic form. In this paper, we show that any maximal isotropic Grassmannian in its Pl\"ucker embedding can be defined by pulling back the equations of $Gr_{\operatorname{iso}}(3,7)$ or $Gr_{\operatorname{iso}}(4,8)$.