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Parametrizing maximal compact subvarieties

Authors:	Jodie D Novak

Institution:	Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078-0613

Abstract:	For the Lie group $G = Sp(n, {\mathbb R} )$ , let be the open orbit of Lagrangian planes of signature in the generalized flag variety of Lagrangian planes in ${\mathbb C} ^{2n}$ . For a suitably chosen maximal compact subgroup of and a base point we have that the orbit of is a maximal compact subvariety of . We show that for $i = 1, \dots , n-1$ the connected component containing in the space of ${G_{\mathbb C}}$ translates of which lie in is biholomorphic to $G/K \times {\overline{G/K}}$ , where ${\overline{G/K}}$ denotes with the opposite complex structure.

Keywords:	Generalized flag variety Penrose transform symplectic group

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