BASIC POLYNOMIAL INVARIANTS, FUNDAMENTAL REPRESENTATIONS AND THE CHERN CLASS MAP

Abstract

Consider a crystallographic root system together with its Weyl group W acting on the weight lattice Lambda. Let Z[Lambda](W) and S (Lambda)(W) be the W-invariant subrings of the integral group ring Z[Lambda] and the symmetric algebra S (Lambda) respectively. A celebrated result by Chevalley says that Z[Lambda](W) is a polynomial ring in classes of fundamental representations rho(1), ... , rho(n) and S (Lambda)(W) circle times Q is a polynomial ring in basic polynomial invariants q(1), ... , q(n). In the present paper we establish and investigate the relationship between rho(i)'s and q(i)'s over the integers. As an application we provide estimates for the torsion of the Grothendieck gamma-filtration and the Chow groups of some twisted flag varieties up to codimension 4.