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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