Envelopes and classifying spaces

Nikita A. Karpenko

Mathematische Nachrichten, 2023, vol. 296, issue 10, 4769-4777

Abstract: For a split semisimple algebraic group H with its split maximal torus S, let f:CH(BH)→CH(BS)W$f: \mathop {\mathrm{CH}}\nolimits (\mathcal {B}H)\rightarrow \mathop {\mathrm{CH}}\nolimits (\mathcal {B}S)^W$ be the restriction homomorphism of the Chow rings CH$\mathop {\mathrm{CH}}\nolimits$ of the classifying spaces B$\mathcal {B}$ 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.

Date: 2023
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