Whitney regularity of the image of the Chevalley mapping. Issue 5 (13th July 2016)

• Record Type: Journal Article
• Authors: Barbançon, Gérard P.
• Is Part Of: Proceedings. Volume 146:Issue 5(2016)
• Page Start: 895
• Page End: 904
• Publication Date: 2016-07-13
• Subjects: Whitney 1-regularity, -- finite reflection groups, -- Morse theory, -- finite class of differentiability; Primary 20F55, -- 58B10, -- Secondary 37B, -- 57R; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210515000839
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : A compact set K ⊂ ℝ n is Whitney 1-regular if 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 paper gives the Whitney 1-regularity of the image by P of any closed ball centred at the origin. The proof uses the works of Givental', Kostov and Arnol'd on the symmetric group. It needs a generalization of a property of the Vandermonde determinants to the Jacobian of the Chevalley mappings.