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Proceedings of the American Mathematical Society

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Parametrizing maximal compact subvarieties

Author: Jodie D. Novak
Journal: Proc. Amer. Math. Soc. 124 (1996), 969-975
MSC (1991): Primary 22E46; Secondary 22E45
MathSciNet review: 1301042
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Abstract: For the Lie group $G = Sp(n, {\mathbb R} )$, let $D_i $ be the open $G-$orbit of Lagrangian planes of signature $(i,n-i)$ in the generalized flag variety of Lagrangian planes in ${\mathbb C} ^{2n}$. For a suitably chosen maximal compact subgroup $K$ of $G$ and a base point $x_i$ we have that the $K-$orbit of $x_i$ is a maximal compact subvariety of $D_i $. We show that for $i = 1, \dots , n-1$ the connected component containing $Kx_i $ in the space of ${G_{\mathbb C}} $ translates of $Kx_i $ which lie in $D_i $ is biholomorphic to $G/K \times {\overline{G/K}}$, where ${\overline{G/K}}$ denotes $G/K$ with the opposite complex structure.

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Additional Information

Jodie D. Novak
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613
Address at time of publication: Department of Mathematical Sciences, Ball State University, Muncie,Indiana 47303

Keywords: Generalized flag variety, Penrose transform, symplectic group
Received by editor(s): August 16, 1994
Communicated by: Roe Goodman
Article copyright: © Copyright 1996 American Mathematical Society