In my talk I introduce a certain noncommutative inhomogeneous quadratic algebra and distinguish set of mutually commuting element in it in such a way that three kinds of Dunkl operators a t critical level will corresponds to some representations of the quadratic algebra in question. The main purpose of my talk is to explain some algebraic and combinatorial properties of that "universal Dunkl elements" (UDE), as well as to outlook surprising connections of UDE with quantum and classical Schubert calculus, elliptic hypergeometric series, volume of Chan-Robbins polytopes and so on.