1. Generalised symmetries and bases for Dunkl monogenics
- Author
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De Bie, Hendrik, Langlois-Rémillard, Alexis, Oste, Roy, and Van der Jeugt, Joris
- Subjects
Mathematics - Representation Theory ,Mathematics - Classical Analysis and ODEs ,20F55, 43A32, 30G35, 33C52, 33C55 - 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., Comment: 18 pages, typos corrected, authors's accepted version for publication in Rocky Mountain J. Math
- Published
- 2022
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