Orthogonal basis for spherical monogenics by step two branching

2010/10/08 by R. Lavicka, Roman Lávička, Vladimı́r Souček +5
Mathematics · #22E70 #30G35 #33C45 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:22E70 #msc:30G35 #msc:33C45

paper · pdf · doi:10.48550/arxiv.1010.1620

submitted

arxiv created 2010/10/08 · openalex publication_date 2010/10/08 · arxiv updated 2010/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R^m. They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on R^m. Fix the direct sum R^m = R^p x R^q. In this paper we will study the decomposition of the space M_n(R^m;C_m) of spherical monogenics of order n under the action of Spin(p) x Spin(q). As a result we obtain a Spin(p) x Spin(q)-invariant orthonormal basis for M_n(R^m;C_m). In particular, using the construction with p = 2 inductively, this yields a new orthonormal basis for the space M_n(R^m;C_m).

Citations

• Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3
• The Gelfand-Tsetlin bases for spherical monogenics in dimension 3

Related

• Generating functions for spherical harmonics and spherical monogenics
• Constructing 3-Dimensional Monogenic Homogeneous Functions
• Complete orthogonal Appell systems for spherical monogenics
• The Gelfand-Tsetlin bases for spherical monogenics in dimension 3
• The orthogonal branching problem for symplectic monogenics