Geodesic
Basic polynomial invariants, fundamental representations and the Chern class map
Documenta mathematica, Tome 17 (2012), pp. 135-150
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Consider a crystallographic root system together with its Weyl group W acting on the weight lattice Λ. Let Z[Λ]W and S(Λ)W be the W-invariant subrings of the integral group ring Z[Λ] and the symmetric algebra S(Λ) respectively. A celebrated result by Chevalley says that Z[Λ]W is a polynomial ring in classes of fundamental representations ρ1​,...,ρn​ and S(Λ)W⊗Q is a polynomial ring in basic polynomial invariants q1​,...,qn​. In the present paper we establish and investigate the relationship between ρi​'s and qi​'s over the integers. As an application we provide estimates for the torsion of the Grothendieck γ-filtration and the Chow groups of some twisted flag varieties up to codimension 4.
DOI : 10.4171/dm/363
Classification : 13A50, 14L24
Mots-clés : torsion, Dynkin index, polynomial invariant, fundamental representation, Chow group, gamma-filtration, twisted flag variety 
@article{10_4171_dm_363,
     author = {Erhard Neher and Sanghoon Baek and Kirill Zainoulline},
     title = {Basic polynomial invariants, fundamental representations and the {Chern} class map},
     journal = {Documenta mathematica},
     pages = {135--150},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/363},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/363/}
}
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Erhard Neher; Sanghoon Baek; Kirill Zainoulline. Basic polynomial invariants, fundamental representations and the Chern class map. Documenta mathematica, Tome 17 (2012), pp. 135-150. doi: 10.4171/dm/363

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