Rational Mackey Functors for Compact Lie Groupsi

A rational Mackey functor M for a compact Lie group G can be viewed as a collection of sheaves on spaces of conjugacy classes of subgroups, one for each closed subgroup H, related by restriction maps only. This in turn may be speciied by giving a suitably continuous family consisting of a Q 0 (W G (H))-module V (H) for each closed subgroup H with restriction maps V (^ K) ?! V (K) whenever K is normal in ^ K and ^ K=K is a torus (a `continuous Weyl-toral module'). In Part I we show that the category of rational Mackey functors is equivalent to the category of rational continuous Weyl-toral modules. In Part II we use this result to give an algebraic analysis of the category of rational Mackey functors, showing in particular that it has homological dimension equal to the rank of the group.