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$\mathrm{Sp}_n(q)$-conjugacy classes in $\mathrm{GL}_{2n}(q)$
The symplectic group $\mathrm{Sp}_n(q)$ acts on $\mathrm{GL}_{2n}(q)$ by conjugation. All the literature I have found concerning the orbits of action of this kind is "Unipotent conjugacy classes in ...
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