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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 outthe Lagrangian-Grassmannian variety $L(n,2n)$ of maximal isotropic subspaces ina symplectic vector space of dimension $2n$ in the Grassmannian variety$G(n,2n)$

An explicit description in terms of Pl\"ucker coordinates of the Langrangian-Grassmannian