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Timeline for Is SO(2n+1)/U(n) a symmetric space?

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Jun 20, 2016 at 21:02 comment added Ninnat Dangniam Sorry. I meant the looser sense in which both $SO(2n)/U(n)$ and $SO(2n+1)/U(n)$ are symmetric.
Jun 20, 2016 at 21:01 comment added Claudio Gorodski Conjugation with a fixed complex structure $J$ on $\mathbb R^{2n}$ defines an involutive automorphism of $SO(2n)$ whose fixed point set is precisely $U(n)$.
Jun 20, 2016 at 20:58 comment added Ninnat Dangniam I hope you don't mind if I have to take a step back. In which sense is $SO(2n)/U(n)$ symmetric then?
Jun 20, 2016 at 20:34 history edited Claudio Gorodski CC BY-SA 3.0
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Jun 20, 2016 at 20:28 history answered Claudio Gorodski CC BY-SA 3.0