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A uniform description of compact symmetric spaces as Grassmannians using the magic square

Conan Leung Chinese Univ of HK Yongdong Huang Jinan University

Differential Geometry mathscidoc:1608.10082

Math. Ann., (350), 79-106, 2011
Suppose A and B are normed division algebras, i.e. R,C,H or O, we introduce and study Grassmannians of linear subspaces in (A ⊗ B)n which are complex/Lagrangian/maximal isotropic with respect to natural two tensors on (A ⊗ B)n. We show that every irreducible compact symmetric space must be one of these Grassmannian spaces, possibly up to a finite cover. This gives a simple and uniform description of all compact symmetric spaces. This generalizes the Tits magic square description for simple Lie algebras to compact symmetric spaces.
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@inproceedings{conan2011a,
  title={A uniform description of compact symmetric spaces as Grassmannians using the magic square},
  author={Conan Leung, and Yongdong Huang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160830140754243751551},
  booktitle={Math. Ann.},
  number={350},
  pages={79-106},
  year={2011},
}
Conan Leung, and Yongdong Huang. A uniform description of compact symmetric spaces as Grassmannians using the magic square. 2011. In Math. Ann.. pp.79-106. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160830140754243751551.
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