Generalised symmetries and bases for Dunkl monogenics

Abstract

We introduce a family of commuting generalised symmetries of the Dunkl--Dirac operator inspired by the Maxwell construction in harmonic analysis. We use these generalised symmetries to construct bases of the polynomial null-solutions of the Dunkl--Dirac operator. These polynomial spaces form representation spaces of the Dunkl--Dirac symmetry algebra. For the ${\mathbb{Z}}_2^d$ case, the results are compared with previous investigations.

18 pages, typos corrected, authors's accepted version for publication in Rocky Mountain J. Math

References in corpus (1)

• Finite-dimensional representations of the symmetry algebra of the dihedral Dunkl--Dirac operator

Cited by in corpus (1)

• Dunkl symplectic algebra in generalized Calogero models