Generalised symmetries and bases for Dunkl monogenics

Autor:	De Bie, Hendrik, Langlois-Rémillard, Alexis, Oste, Roy, Van der Jeugt, Joris
Rok vydání:	2022
Předmět:	Mathematics - Representation Theory Mathematics - Classical Analysis and ODEs 20F55 43A32 30G35 33C52 33C55
Zdroj:	Rocky Mountain J. Math. 53 (2) 397-415 (2023)
Druh dokumentu:	Working Paper
DOI:	10.1216/rmj.2023.53.397
Popis:	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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.01204 Zobrazit plný text záznamu View this record from Arxiv