On $H^{\ast }(BP{U}_n;\mathbb{Z})$ and Weyl group invariants

Abstract

For the projective unitary group $P{U}_n$ with a maximal torus $T_{P{U}_n}$ and Weyl group $W$, we show that the integral restriction homomorphism \[ρ_{PU_n} \colon H^*(BPU_n;\mathbb{Z})\rightarrow H^*(BT_{PU_n};\mathbb{Z})^W\] to the integral invariants of the Weyl group action is onto. We also present several rings naturally isomorphic to $H^{\ast }(B{T}_{P{U}_n};\mathbb{Z}{)}^W$. In addition we give general sufficient conditions for the restriction homomorphism $\ddot{I}{}_G$ to be onto for a connected compact Lie group $G$.

26 pages. Final version