Compact weakly symmetric spaces and spherical pairs

Nguyêñ, H.

doi:10.1090/S0002-9939-00-05425-3

Compact weakly symmetric spaces and spherical pairs
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by H. D. Nguyêñ PDF

Proc. Amer. Math. Soc. 128 (2000), 3425-3433 Request permission

Abstract:

Let $(G,H)$ be a spherical pair and assume that $G$ is a connected compact simple Lie group and $H$ a closed subgroup of $G$. We prove in this paper that the homogeneous manifold $G/H$ is weakly symmetric with respect to $G$ and possibly an additional fixed isometry $\mu$. It follows that M. Krämer’s classification list of such spherical pairs also becomes a classification list of compact weakly symmetric spaces. In fact, our proof involves a case-by-case study of the isotropy representations of all spherical pairs on Krämer’s list.

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