INTEGRAL WEYL INVARIANTS AND THE BOREL HOMOMORPHISM FOR SPIN(N)

We examine the Weyl invariant subring H(BT)(W) of the integral singul ar cohomology ring H(BT) of the classifying space BT of the maximal t orus T in a connected compact Lie group K. We show that H(BT)(W) is n ot a polynomial algebra for K = Spin(n) when n greater than or equal t o 10. We describe the connection of this result with the Borel homomor phism H(BT) --> H*(K/T).