RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES

Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always an algebraic model. Based on this idea, we show local systems connected finite loop space simple When arises from group, recovers special case result Pol and Williamson about cofree $G$-spectra. More generally, if $K$ is closed subgroup $G$ such Weyl $W_GK$ connected, then certain $G$-spectra `at $K$' For example, when trivial just $G$-spectra, aforementioned result. Throughout, pay careful attention to role torsion complete categories.