96-14
Rings of Generalized and Stable Invariants and Classifying Spaces of Compact Lie Groups
by Neumann, F.; Neusel, M.D.; Smith, L.
Preprint series: 96-14, Preprints
- MSC:
- 13A50 Invariant theory, See also {14D25}
- 55R40 Homology of classifying spaces, characteristic classes, See also {57Txx, 57R20}
- 57T10 Homology and cohomology of Lie groups
Abstract: Let G be a compact connected Lie group with maximal torus T ,!G and Weyl group WG . There is the fibrationG j\Gamma! G=T k\Gamma! BTand we show that the Eilenberg-Moore spectral sequence mod p, foran odd prime p, of this fibration collapses at the term E 2 . As animportant step in the proof we compute the kernel of the inducedmapker f(k \Lambda ) : H \Lambda (BT ; F p ) \Gamma! H \Lambda (G=T; F p )gand 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 bymeans of the action of WG on H \Lambda (BT ; F p ) the odd primes p forwhich H \Lambda (BG; Z) has p-torsion.