Compact weakly symmetric spaces and spherical pairs

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    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 μ. 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.

    Original languageEnglish (US)
    Pages (from-to)3425-3433
    Number of pages9
    JournalProceedings of the American Mathematical Society
    Volume128
    Issue number11
    DOIs
    StatePublished - 2000

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)
    • Applied Mathematics

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