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Whitney regularity of the image of the Chevalley mapping
- Source :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 146:895-904
- Publication Year :
- 2016
- Publisher :
- Cambridge University Press (CUP), 2016.
-
Abstract
- A compact set K ⊂ ℝn 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.
Details
- ISSN :
- 14737124 and 03082105
- Volume :
- 146
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Accession number :
- edsair.doi.dedup.....3bb232f54ff8444939eb04bda6cd15ad