Let us be given a symplectic space of dimension $2n$ $(V, w)$. Symplectic equivalent subspaces $L_1, L_2$ are such subspaces $V$ for which there exists a symplectic operator $A$ such that $L_1=AL_2$. The question is as follows: how many symplectic nonequivalent subspaces of a given dimension $l$ exist. I know that two arbitrary symplectic subspaces are symplectic equivalent if the constraints of the original symplectic form on them have the same rank. I read here about what the rank of a symplectic form is, but it did not become clearer how to count the number of such subspaces.
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