Could someone tell me where to find a proof of the following statement that I found in some notes about characteristic classes I was reading?
If $G$ is a compact connected Lie group with maximal torus $T$ and Weyl group $W$ and if $H^∗(G)$ has no torsion for any prime $p$ that divides the order of $W$, then $H^∗ (BG) ∼= H^{∗} (BT )^W .$
Thank you
A proof can be found in Topology of Lie Groups I and II by Mimura and Toda, Ch VII Th 3.29. It can also be found in the works of Borel, in particular his springer notes. But the Mimura and Toda book gives the same proofs and Borel, just a little easier to read.