Orthogonal basis for spherical monogenics by step two branching
type: Item
instance of: scholarly article
title: Orthogonal basis for spherical monogenics by step two branching
zbMATH Open document ID: 1250.30048
author: Roman Lávička
author: Vladimír Souček
author: Peter van Lancker
published in: Annals of Global Analysis and Geometry
publication date: 2012-02-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1010.1620
full work available at URL: LU-2154824
review text: The authors study higher dimensional function theory of monogenic functions; for references to the theory see [\textit{F. Brackx, R. Delanghe} and \textit{F. Sommen}, Clifford analysis. Research Notes in Mathematics, 76. Boston-London-Melbourne: Pitman Advanced Publishing Program (1982; Zbl 0529.30001); \textit{R. Delanghe, F. Sommen} and \textit{V. Souček}, Clifford algebra and spinor-valued functions. A function theory for the Dirac operator. Related REDUCE software by F. Brackx and D. Constales. Mathematics and its Applications (Dordrecht). 53. Dordrecht etc.: Kluwer Academic Publishers (1992; Zbl 0747.53001); \textit{J. Gilbert} and \textit{M. A. M. Murray}, Clifford algebras and Dirac operators in harmonic analysis. Cambridge (UK): Cambridge University Press (1991; Zbl 0733.43001)]. The aim of this publication is to study the decomposition of spherical harmonics and monogenics under the action of \(\text{Spin}(p)\times \text{Spin}(q)\). The authors also obtain an orthonormal basis for spherical harmonics and monogenics. The key tool is the Fischer decomposition. Another construction of \(\text{Spin}(p)\times \text{Spin}(q)\)-invariant spaces of monogenic functions is given in [\textit{A. K. Common} and \textit{F. Sommen}, J. Math. Anal. Appl. 185, No. 1, 189--206 (1994; Zbl 0822.30003); \textit{G. Jank} and \textit{F. Sommen}, Complex Variables, Theory Appl. 13, No. 3--4, 195--212 (1990; Zbl 0703.30044); \textit{F. Sommen}, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 21, 295--323 (1989; Zbl 0709.35077)].
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 22E70
zbMATH DE Number: 6006614
zbMATH Keywords: Clifford analysis
zbMATH Keywords: Dirac operators
zbMATH Keywords: representations
zbMATH Keywords: branching rules
zbMATH Keywords: spin groups
MaRDI profile type: Publication
OpenAlex ID: W2162455001
arXiv ID: 1010.1620
cites work: On Casimir's ghost
cites work: Q3048980
cites work: On a generalized Appell system and monogenic power series
cites work: Gelfand-Tsetlin bases for spherical monogenics in dimension 3
cites work: The Howe dual pair in Hermitean Clifford analysis
cites work: Special bi-axial monogenic functions
cites work: Q4003806
cites work: An explicit realization of spinor spaces and its application to clifford analysis
cites work: Q5795545
cites work: Q3995205
cites work: Q4382291
cites work: Q3223062
cites work: Transcending Classical Invariant Theory
cites work: Remarks on Classical Invariant Theory
cites work: Bases for some reciprocity algebras. II
cites work: Clifford analysis, biaxial symmetry and pseudoanalytic functions
cites work: Gelfand–Tsetlin Bases for Classical Lie Algebras
cites work: Spherical harmonics
cites work: Spherical monogenic functions and analytic functionals on the unit sphere
cites work: Q3492066
cites work: Q5494113
cites work: On the Segal-Shale-Weil representations and harmonic polynomials
cites work: Spherical monogenics: An algebraic approach
cites work: Models for irreducible representations of Spin\((m)\)
cites work: Q5521058
cites work: On quantum methods in the representation theory of reductive Lie algebras
DOI: 10.1007/S10455-011-9276-Y
description: scientific article