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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Holomorphic actions of $\textrm {Sp}(n, \textbf {R})$ with noncompact isotropy groups
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by Hugo Rossi
Trans. Amer. Math. Soc. 263 (1981), 207-230
DOI: https://doi.org/10.1090/S0002-9947-1981-0590420-X

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