by Neumann, F., Neusel, M.D., Smith, L..

**Series:** 1996-14, Preprints

- MSC:
- 13A50 Actions of groups on commutative rings; invariant theory
- 55R40 Homology of classifying spaces, characteristic classes
- 57T10 Homology and cohomology of Lie groups

**Abstract:**

G be a compact connected Lie group with maximal torus T ,!

G and Weyl group WG . There is the fibration

G j

\Gamma! G=T k

\Gamma! BT

and we show that the Eilenberg-Moore spectral sequence mod p, for

an odd prime p, of this fibration collapses at the term E 2 . As an

important step in the proof we compute the kernel of the induced

map

ker f(k \Lambda ) : H \Lambda (BT ; F p ) \Gamma! H \Lambda (G=T; F p )g

and identify it with the ideal J1 (WG ) ae H \Lambda (BT ; F p ) of stable in-

variants of the Weyl group. We apply our results to determine by

means of the action of WG on H \Lambda (BT ; F p ) the odd primes p for

which H \Lambda (BG; Z) has p-torsion.

**Keywords:**