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Title: Canonical bases for $\mathfrak{sl}(2,{\mathbb{C}})$-modules of spherical monogenics in dimension 3 (English)
Author: Lávička, Roman
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 46
Issue: 5
Year: 2010
Pages: 339-349
Summary lang: English
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Category: math
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Summary: Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as ${\mathfrak{sl}}(2,{\mathbb{C}})$-modules. As finite-dimensional irreducible ${\mathfrak{sl}}(2,{\mathbb{C}})$-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. Gürlebeck in [3]. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials. (English)
Keyword: spherical monogenics
Keyword: orthogonal basis
Keyword: Legendre polynomials
Keyword: $\mathfrak{sl}(2,{\mathbb{C}})$-module
MSC: 17B10
MSC: 30G35
MSC: 33C50
idZBL: Zbl 1249.30136
idMR: MR2753988
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Date available: 2010-12-14T15:06:33Z
Last updated: 2013-09-19
Stable URL: http://hdl.handle.net/10338.dmlcz/141388
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