Parametrizing maximal compact subvarieties
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- by Jodie D. Novak PDF
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Abstract:
For the Lie group $G = \mathrm {Sp}(n, \mathbb {R} )$, 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.References
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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
- Email: novak@math.bsu.edu
- Received by editor(s): August 16, 1994
- Communicated by: Roe Goodman
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 969-975
- MSC (1991): Primary 22E46; Secondary 22E45
- DOI: https://doi.org/10.1090/S0002-9939-96-03153-X
- MathSciNet review: 1301042