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

Roman Lávička

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 5, page 339-349
  • ISSN: 0044-8753

Abstract

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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. Gürlebeck in [3]. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.

How to cite

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Lávička, Roman. "Canonical bases for $\mathfrak {sl}(2,{\mathbb {C}})$-modules of spherical monogenics in dimension 3." Archivum Mathematicum 046.5 (2010): 339-349. <http://eudml.org/doc/116497>.

@article{Lávička2010,
abstract = {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.},
author = {Lávička, Roman},
journal = {Archivum Mathematicum},
keywords = {spherical monogenics; orthogonal basis; Legendre polynomials; $\mathfrak \{sl\}(2,\{\mathbb \{C\}\})$-module; spherical monogenics; orthogonal basis; Legendre polynomials; -module},
language = {eng},
number = {5},
pages = {339-349},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Canonical bases for $\mathfrak \{sl\}(2,\{\mathbb \{C\}\})$-modules of spherical monogenics in dimension 3},
url = {http://eudml.org/doc/116497},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Lávička, Roman
TI - Canonical bases for $\mathfrak {sl}(2,{\mathbb {C}})$-modules of spherical monogenics in dimension 3
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 5
SP - 339
EP - 349
AB - 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.
LA - eng
KW - spherical monogenics; orthogonal basis; Legendre polynomials; $\mathfrak {sl}(2,{\mathbb {C}})$-module; spherical monogenics; orthogonal basis; Legendre polynomials; -module
UR - http://eudml.org/doc/116497
ER -

References

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