I have found this exercise in Dusa McDuff "Introduction to symplectic topology" (2.3.6). I don't see the way how to prove it. It hasn't coordinates where I can to check this, and also it's not the case of the theorem about closed subgroup of Lie group.
2026-03-28 23:59:42.1774742382
How to prove that $Sym(n, \mathbb{C}) \cap U(n) $ is a submanifold of $U(n)$?
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