Embedding Factors for Branching in Hermitian Clifford Analysis

2013/05/16 by F. Brackx, Fred Brackx, H. De Schepper +9 · 1 citation
Mathematics · #30G35 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30G35

paper · pdf · doi:10.48550/arxiv.1305.3698

submitted. arXiv admin note: text overlap with arXiv:1102.4211

arxiv created 2013/05/16 · openalex publication_date 2013/05/16 · arxiv updated 2013/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A step 2 branching decomposition of spaces of homogeneous Hermitian monogenic polynomials in Cⁿ is established with explicit embedding factors in terms of the generalized Jacobi polynomials, which allows for an inductive construction of an orthogonal basis for those spaces. The embedding factors and the orthogonal bases are fully worked out in the complex dimension 2 case, with special interest for the Appell property.

Citations

• Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3
• The Gelfand-Tsetlin bases for spherical monogenics in dimension 3
• Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces

Cited by

• Clifford-Appell formulation of a Dirac-type Kronig-Penney model in condensed matter physics

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