Fischer decomposition for the symplectic group
type: Item
instance of: scholarly article
title: Fischer decomposition for the symplectic group
zbMATH Open document ID: 1390.30054
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-11-02T00:00:00Z
full work available at URL: https://biblio.ugent.be/publication/8562030
review text: \textit{F. Brackx} et al. [Math. Methods Appl. Sci. 39, No. 16, 4874--4891 (2016; Zbl 1361.30085)] conjectured a form for the Fischer decomposition for the spinor-valued polynomials defined on Euclidean space of four-fold dimension in terms of spaces \(S^r_{a,b}\) of bi-homogeneous \(\text{osp}(4|2)\)-monogenic polynomials with values in the symplectic cell \(S^r_r\). The current paper formulates and proves a corrected version of this Fischer decomposition which holds in ALL cases. Also shown, using the spirit of \textit{R. Howe} [Trans. Am. Math. Soc. 313, No. 2, 539--570 (1989; Zbl 0674.15021)], is the \(\mathrm{Sp}(p)\)-irreducibility of the spaces \(S^r_{a,b}\). As preparatory for the latter deduction a special section presenting refinements of Clifford analysis through the concept of symmetry reduction is included in the paper.
reviewed by: Linda R. Sons
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 6802346
zbMATH Keywords: quaternionic Clifford analysis
zbMATH Keywords: Fischer decomposition
author: F. Brackx
author: H. De Schepper
author: D. Eelbode
author: Roman Lávička
author: Vladimír Souček
MaRDI profile type: Publication
OpenAlex ID: W2761446107
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DOI: 10.1016/J.JMAA.2017.09.041
description: scientific article; zbMATH DE number 6802346