14-14 Gerard P. Barbanson
Whitney Regularity of the Image of the Chevalley Mapping (43K, AMS - LaTeX) Mar 17, 14
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Abstract. A closed set \$F\$ is Whitney 1-regular if for each compact \$K\subset F\$, the geodesic distance in \$K\$ is equivalent to the Euclidean distance. Let \$P\$ be the Chevalley map defined by an integrity basis of the algebra of polynomials invariant by a reflection group, this note gives the Whitney regularity of the image \$P({\mathbb R}^n)\$. The proof uses ideas in [1], [3], [7] and [8] and needs a generalization to the Jacobian of the Chevalley mappings of a property of Van der Monde determinants.

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