Abstract
When a compact connected Lie group acts smoothly on a manifold X with only connected isotropy subgroups of maximal rank, the action is completeley determined by the corresponding action of its Weylgroup WG on the fixed space XT of the maximal torus. Isotropy subgroups of such actions are determined.
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Hauschild, V. Compact lie group actions with isotropy subgroups of maximal rank. Manuscripta Math 34, 355–379 (1981). https://doi.org/10.1007/BF01165545
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DOI: https://doi.org/10.1007/BF01165545