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

2010/03/29 by Roman Lávička, Roman Lavicka, Lavicka, Roman · 2 citations
Mathematics · #30G35 #33C50 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Representation Theory (math.RT) #math.CV #math.RT #msc:30G35 #msc:33C50

paper · pdf · doi:10.48550/arxiv.1003.5587

a revised version (some references added, Introduction changed ); accepted for publication in Proceedings of the Winter School, Srni, Czech Republic, 2010

openalex publication_date 2010/03/29 · arxiv created 2010/06/17 · arxiv updated 2010/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as sl(2,C)-modules. As finite-dimensional irreducible sl(2,C)-modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Guerlebeck. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.

Citations

• On the development of Bohr's phenomenon in the context of Quaternionic analysis and related problems
• The Gelfand-Tsetlin bases for spherical monogenics in dimension 3

Cited by

• Embedding Factors for Branching in Hermitian Clifford Analysis
• Orthogonal basis for spherical monogenics by step two branching

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