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How to prove Siegel upper half plane is a hermitian symmetric space

There is a statement that is Siegel upper half plane of genus g, $\mathbb{H}_g:=\left\{Z=X+i Y \in M_n(\mathbb{C}) \mid X, Y \text { real }, Z=Z^{T}, Y=\operatorname{Im} Z>0\right)$ is isomorphic ...
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