Universal equations for Lagrangian and isotropic Grassmannians

It is known that any ordinary Grassmannian Gr(k,n) in its Plücker embedding is set-theoretically (but not scheme-theoretically) cut out by pulling back the unique defining equation of Gr(2,4) along natural projection and contraction maps. We prove an analogous result for Lagrangian and isotropic Grassmannians. This talk is based on joint work with Nafie Tairi.