The Dunkl intertwining operator

Abstract

We consider Dunkl theory associated to a general Coxeter group G. A new characterization of the regularity of the weight k is given and a new construction, devoid of Kozul complex theory, of the Dunkl intertwining operator V k is established. We apply our results to derive sharp estimates of the Dunkl kernel. We give explicit formula in the case of orthogonal positive root systems.