Dunkl-Type Operators with Projection Terms Associated to Orthogonal Subsystems in Root System

Abstract

In this paper, we introduce a new differential-difference operator Tξ (ξ∈RN) 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 Tξ and the directional derivative ∂ξ. In the case of one variable, we prove that the Kummer functions are eigenfunctions of this operator.