Abstract
In this paper, we introduce a new differential-difference operator T-xi (xi is an element of R-N) by using projections associated to orthogonal subsystems in root systems. Similarly to Dunkl theory, we show that these operators commute and we construct an intertwining operator between T-xi and the directional derivative partial derivative(xi). In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator.