Grassmannians of symplectic subspaces
type: Item
instance of: scholarly article
title: Grassmannians of symplectic subspaces
zbMATH Open document ID: 1246.37078
author: Jae-Hyouk Lee
author: Naichung Conan Leung
published in: Manuscripta Mathematica
publication date: 2011-11-08T00:00:00Z
review text: Let \((V, \omega )\) be a symplectic vector space of dimension \(2n\). The set of all \(2k\)-dimensional linear subspaces in \(V\) which are symplectic with respect to \(\omega \) is called the symplectic Grassmannian \(Gr^{Sp}(2k, 2n)\). The objective of this paper is to study the geometry of \(Gr^{Sp}(2k, 2n)\). A main tool introduced by the authors is the symplectic twistor Grassmannian \(\hat{{\mathcal T}}(2k, 2n)\) which is the set of triples \((S, J_S, J_{S^{\omega }})\) with \(S\in Gr^{Sp}(2k, 2n)\) and \(J_S\) (respectively \(J_{S^{\omega }}\)) a compatible complex structure on \(S\) (respectively \(S^{\omega }\)). Symplectic and Lagrangian submanifolds are then obtained in \(Gr^{Sp}(2k, 2n)\) as special kinds of Schubert cycles.
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 14M15
Mathematics Subject Classification ID: 53D12
zbMATH DE Number: 5968966
zbMATH Keywords: Grassmannian of symplectic subspaces
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
full work available at URL: s00229-011-0448-7
OpenAlex ID: W2076925422
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cites work: Q4192639
DOI: 10.1007/S00229-011-0448-7
description: scientific article; zbMATH DE number 5968966