An explicit description in terms of Pl\"ucker coordinates of the   Langrangian-Grassmannian
  For an arbitrary field of any characteristic we give an explicit description, in terms of Pl\"ucker coordinates, of the projective linear space that cuts out the Lagrangian-Grassmannian variety $L(n,2n)$ of maximal isotropic subspaces in a symplectic vector space of dimension $2n$ in the Grassmannian variety $G(n,2n)$ 
J. Carrillo-Pacheco, F. Jarqu\'in-Z\'arate, M. Velasco-Fuentes and F.   Zald\'ivar
math.SG