Note on restriction maps of Chow rings to Weyl group invariants

TL;DR

This paper investigates the restriction map from the Chow ring of the classifying space of an algebraic group to the invariants under the Weyl group, highlighting cases where surjectivity fails, especially for simply connected groups with torsion.

Contribution

It provides new insights into the behavior of the restriction map in Chow rings, particularly identifying conditions under which it is not surjective.

Findings

Restriction map is not surjective for simply connected groups with torsion in H(G)

Analysis of the restriction map's properties in relation to Weyl group invariants

Clarification of the algebraic structure of Chow rings for classifying spaces

Abstract

Let G be an algebraic group corresponding to a compact Lie group. We study the restiction map from the Chow ring CH(BG) to the Wely group invariants CH(BT)^W. For example, we note that if G is simply connect and H(G) has torsion, then the restriction map is always not surjective.