Abstract
If G G is a compact, connected Lie group, the isotropy subgroups of the adjoint representation of G G are connected and the dimension of the fixed point set of a maximal torus of G G is equal to the the rank of G G . Results similar to these are given when G G acts differentiably on an integral cohomology sphere and has the adjoint representation as weak linear model. This is done by analyzing an induced action of the Weyl group of G G .
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