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### How to characterize the dual of an isotropic hyperplane?

Hi there! I have a very simple question, which requires an expert in multilinear algebra.
$V$ is an $n$-dimensional vector space, and $\omega\in V^\ast\wedge V^\ast$ is a skew-symmetric form on it. ...

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### Image of an isotropic manifold under lagrangian correspondence is isotropic?

Is the following statement well known?
Let $M,N$ be symplectic (algebraic) manifolds. Let $L \subset M \times N$ be a (smooth)
Lagrangian correspondence. For a subset $X \subset M$ we denote ...