Transformation groups resembling the adjoint representation

Sullivan, R. W.

doi:10.1090/S0002-9939-1975-0368054-4

Transformation groups resembling the adjoint representation
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Proc. Amer. Math. Soc. 47 (1975), 491-494 Request permission

Abstract:

If $G$ is a compact, connected Lie group, the isotropy subgroups of the adjoint representation of $G$ are connected and the dimension of the fixed point set of a maximal torus of $G$ is equal to the the rank of $G$. Results similar to these are given when $G$ 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 $G$.

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