English

Generalised symmetries and bases for Dunkl monogenics

Representation Theory 2023-09-06 v2 Classical Analysis and ODEs

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 Z2d\mathbb{Z}_2^d case, the results are compared with previous investigations.

Keywords

Cite

@article{arxiv.2203.01204,
  title  = {Generalised symmetries and bases for Dunkl monogenics},
  author = {Hendrik De Bie and Alexis Langlois-Rémillard and Roy Oste and Joris Van der Jeugt},
  journal= {arXiv preprint arXiv:2203.01204},
  year   = {2023}
}

Comments

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

R2 v1 2026-06-24T09:59:32.273Z