April 2023 GENERALISED SYMMETRIES AND BASES FOR DUNKL MONOGENICS
Hendrik De Bie, Alexis Langlois-Rémillard, Roy Oste, Joris Van der Jeugt
Rocky Mountain J. Math. 53(2): 397-415 (April 2023). DOI: 10.1216/rmj.2023.53.397

Abstract

We introduce a family of commuting generalised symmetries of the Dunkl–Dirac operator inspired by the Maxwell construction in harmonic analysis. As an application, 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 2d case, the results are compared with previous investigations.

Citation

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Hendrik De Bie. Alexis Langlois-Rémillard. Roy Oste. Joris Van der Jeugt. "GENERALISED SYMMETRIES AND BASES FOR DUNKL MONOGENICS." Rocky Mountain J. Math. 53 (2) 397 - 415, April 2023. https://doi.org/10.1216/rmj.2023.53.397

Information

Received: 10 March 2022; Accepted: 19 June 2022; Published: April 2023
First available in Project Euclid: 20 June 2023

MathSciNet: MR4604763
zbMATH: 07725144
Digital Object Identifier: 10.1216/rmj.2023.53.397

Subjects:
Primary: 20F55 , ‎43A32
Secondary: 30G35‎ , 33C52 , 33C55

Keywords: Dunkl operator , Dunkl–Dirac equation , generalised symmetries , polynomial monogenics , symmetry algebra , total angular operator

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 2 • April 2023
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