Envelopes and classifying spaces

Abstract

AbstractFor a split semisimple algebraic group H with its split maximal torus S, let be the restriction homomorphism of the Chow rings of the classifying spaces of H and S, where W is the Weyl group. A constraint on the image of f, given by the Steenrod operations, has been applied to the spin groups in a previous paper. Here, we describe and apply to the spin groups another constraint, which is given by the reductive envelopes of H. We also recover in this way some older results on orthogonal groups.