In this paper we begin with the construction of a generalized Segal-Bargmann transform related to every root system with finite reflection group $G.$ To do so, we introduce a Hilbert space $\cal F_k(\C^N)$ of holomorphic functions with reproducing kernel equal to the Dunkl kernel. Moreover, by means of an $\s\l(2)$-triple, we prove the branching decomposition of $\cal F_k(\C^N)$ as a unitary $G\times \widetilde{SL(2,\R)}$-module. Further applications of the $\s\l(2)$-triple to the Dunkl theory are given. This paper is a survey of recent results in [BO3] and [BO4], and it also contains new results.
