Generalised symmetries and bases for Dunkl monogenics

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