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 case, the results are compared with previous investigations.
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