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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Holomorphic actions of $ {\rm Sp}(n,\,{\bf R})$ with noncompact isotropy groups


Author: Hugo Rossi
Journal: Trans. Amer. Math. Soc. 263 (1981), 207-230
MSC: Primary 22E30; Secondary 32N10
MathSciNet review: 590420
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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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DOI: https://doi.org/10.1090/S0002-9947-1981-0590420-X
Article copyright: © Copyright 1981 American Mathematical Society