Geodesic
Basic polynomial invariants, fundamental representations and the Chern class map
Documenta mathematica, Tome 17 (2012), pp. 135-150.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Consider a crystallographic root system together with its Weyl group $W$ acting on the weight lattice $\Lambda$. Let $\ZZ[\Lambda]^W$ and $S(\Lambda)^W$ be the $W$-invariant subrings of the integral group ring $\ZZ[\Lambda]$ and the symmetric algebra $S(\Lambda)$ respectively. A celebrated result by Chevalley says that $\ZZ[\Lambda]^W$ is a polynomial ring in classes of fundamental representations $\rho_1,...,\rho_n$ and $S(\Lambda)^W\otimes\{Q}$ 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.
Classification : 13A50, 14L24
Keywords: Dynkin index, polynomial invariant, fundamental representation, Chow group, gamma-filtration, twisted flag variety, torsion 
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     author = {Baek, Sanghoon and Neher, Erhard and Zainoulline, Kirill},
     title = {Basic polynomial invariants, fundamental representations and the {Chern} class map},
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     pages = {135--150},
     publisher = {mathdoc},
     volume = {17},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a25/}
}
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Baek, Sanghoon; Neher, Erhard; Zainoulline, Kirill. Basic polynomial invariants, fundamental representations and the Chern class map. Documenta mathematica, Tome 17 (2012), pp. 135-150. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a25/