Dunkl-Type Operators with Projections Terms Associated to Orthogonal Subsystems in Roots System

作者：Bouzeffour Fethi^*

来源：Symmetry Integrability and Geometry-Methods and Applications, 2013, 9: 064.

DOI：10.3842/SIGMA.2013.064

• special functions
• differential-difference operators
• integral transforms

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.

• 出版日期2013