Holomorphic actions of 𝑆𝑝(𝑛,𝑅) with noncompact isotropy groups

Rossi, Hugo

doi:10.1090/S0002-9947-1981-0590420-X

Holomorphic actions of $\textrm {Sp}(n, \textbf {R})$ with noncompact isotropy groups
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Trans. Amer. Math. Soc. 263 (1981), 207-230 Request permission

Abstract:

$U(p,q)$ is a subgroup of ${S_p}(n,R)$, for $p + q = n$. ${B_q} = {S_p}(n,r)/U(p,q)$ is realized as an open subset of the manifold of Lagrangian subspaces of ${{\mathbf {C}}^n} \times {{\mathbf {C}}^n}$. It is shown that ${B_q}$ carries a $(pq)$-pseudoconvex exhaustion function. ${B_{pq}} = {S_p}(n,r)/U(p) \times U(q)$ carries two distinct holomorphic structures making the projection to ${B_q}$, ${B_0}$ holomorphic respectively. The geometry of the correspondence between ${B_q}$ and ${B_0}$ via ${B_{pq}}$ is investigated.

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