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Orthogonal basis for spherical monogenics by step two branching

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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 Rm. Fix the direct sum R(m) = R(p) circle plus R(q). In this article, 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)).
Keywords
Branching rules, Clifford analysis, Spin groups, Dirac operators, Representations

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Citation

Please use this url to cite or link to this publication:

Chicago
Lávička, Roman, Vladimir Souček, and Peter Van Lancker. 2012. “Orthogonal Basis for Spherical Monogenics by Step Two Branching.” Annals of Global Analysis and Geometry 41 (2): 161–186.
APA
Lávička, R., Souček, V., & Van Lancker, P. (2012). Orthogonal basis for spherical monogenics by step two branching. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 41(2), 161–186.
Vancouver
1.
Lávička R, Souček V, Van Lancker P. Orthogonal basis for spherical monogenics by step two branching. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. 2012;41(2):161–86.
MLA
Lávička, Roman, Vladimir Souček, and Peter Van Lancker. “Orthogonal Basis for Spherical Monogenics by Step Two Branching.” ANNALS OF GLOBAL ANALYSIS AND GEOMETRY 41.2 (2012): 161–186. Print.
@article{2154824,
  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 Rm. Fix the direct sum R(m) = R(p) circle plus R(q). In this article, 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)).},
  author       = {L{\'a}vi\v{c}ka, Roman and Sou\v{c}ek, Vladimir and Van Lancker, Peter},
  issn         = {0232-704X},
  journal      = {ANNALS OF GLOBAL ANALYSIS AND GEOMETRY},
  keyword      = {Branching rules,Clifford analysis,Spin groups,Dirac operators,Representations},
  language     = {eng},
  number       = {2},
  pages        = {161--186},
  title        = {Orthogonal basis for spherical monogenics by step two branching},
  url          = {http://dx.doi.org/10.1007/s10455-011-9276-y},
  volume       = {41},
  year         = {2012},
}

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