Abstract:
We investigate the complex geometry of a multidimensional generalization $\mathcal{D}(n)$ of the upper-half-plane, which is homogeneous relative the group $G=SL(2n; \mathbb{R})$. For $n>1$ it is the pseudo Hermitian symmetric space which is the open orbit of $G=SL(2n; \mathbb{R})$ on the Grassmanian $Gr_\mathbb{C}(n;2n)$ of $n$-dimensional subspaces of $\mathbb{C}^{2n}$. The basic element of the construction is a canonical covering of $\mathcal{D}(n)$ by maximal Stein submanifolds — horospherical tubes.
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