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

作者：Huang Yongdong; Leung Naichung Conan^*

来源：Mathematische Annalen, 2011, 350(1): 79-106.

DOI：10.1007/s00208-010-0549-8

Suppose A and B are normed algebras, i.e. R, C, H or O, E, we introduce and study Grassmannians of linear subspaces in ( A circle times B)n which are complex/Lagrangian/maximal isotropic with respect to natural two tensors on ( A circle times 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.

• 出版日期2011-5
• 单位香港中文大学