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- W2415199289 abstract "The classical Fischer decomposition of polynomials on Euclidean space makes it possible to express any polynomial as a sum of harmonic poly- nomials multiplied by powers of |x| 2 . A deformation of the Laplace operator was recently introduced by Ch.F. Dunkl. It has the property that the sym- metry with respect to the orthogonal group is broken to a finite subgroup generated by reflections (a Coxeter group). It was shown by B. Orsted and S. Ben Said that there is a deformation of the Fischer decomposition for poly- nomials with respect to the Dunkl harmonic functions. In Cliord analysis, a Dunkl version of the Dirac operator was introduced and studied by P. Cere- jeiras, U. Kahler and G. Ren. The aim of the article is to describe an analogue of the Fischer decomposition for solutions of the Dunkl Dirac operator. The main methods used are coming from representation theory, in particular, from ideas connected with Howe dual pairs." @default.
- W2415199289 created "2016-06-24" @default.
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- W2415199289 date "2009-01-01" @default.
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- W2415199289 title "The Howe Duality for the Dunkl Version of the" @default.
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