Computing with differential-difference operators
The paper shows how Maple can be used to prove identities in the algebra generated be differential-difference operators (Dunkl operators), multiplication by coordinate functions and group translation, essentially in polynomial arithmetic. The proposed technique allows a conceptual proof of a complete orthogonal decomposition of the harmonic polynomials associated with a special case (the abelian reflection groups).
scientific article; zbMATH DE number 1423192