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Fischer decomposition in symplectic harmonic analysis

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Abstract
In the framework of quaternionic Clifford analysis in Euclidean space , which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is obtained in terms of spaces of so-called (adjoint) symplectic spherical harmonics, which are irreducible modules for the symplectic group Sp. Its Howe dual partner is determined to be sl(2, C) circle plus sl(2, C) = so(4, C).
Keywords
Fischer decomposition, Hermitean Clifford analysis, Quaternionic Clifford analysis, Symplectic harmonics, HERMITEAN CLIFFORD ANALYSIS

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

Chicago
Brackx, Fred, Hennie De Schepper, David Eelbode, Roman Lávička, and Vladimir Soucek. 2014. “Fischer Decomposition in Symplectic Harmonic Analysis.” Annals of Global Analysis and Geometry 46 (4): 409–430.
APA
Brackx, Fred, De Schepper, H., Eelbode, D., Lávička, R., & Soucek, V. (2014). Fischer decomposition in symplectic harmonic analysis. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 46(4), 409–430.
Vancouver
1.
Brackx F, De Schepper H, Eelbode D, Lávička R, Soucek V. Fischer decomposition in symplectic harmonic analysis. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. 2014;46(4):409–30.
MLA
Brackx, Fred, Hennie De Schepper, David Eelbode, et al. “Fischer Decomposition in Symplectic Harmonic Analysis.” ANNALS OF GLOBAL ANALYSIS AND GEOMETRY 46.4 (2014): 409–430. Print.
@article{5839780,
  abstract     = {In the framework of quaternionic Clifford analysis in Euclidean space , which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is obtained in terms of spaces of so-called (adjoint) symplectic spherical harmonics, which are irreducible modules for the symplectic group Sp. Its Howe dual partner is determined to be sl(2, C) circle plus sl(2, C) = so(4, C).},
  author       = {Brackx, Fred and De Schepper, Hennie and Eelbode, David and L{\'a}vi\v{c}ka, Roman and Soucek, Vladimir},
  issn         = {0232-704X},
  journal      = {ANNALS OF GLOBAL ANALYSIS AND GEOMETRY},
  keyword      = {Fischer decomposition,Hermitean Clifford analysis,Quaternionic Clifford analysis,Symplectic harmonics,HERMITEAN CLIFFORD ANALYSIS},
  language     = {eng},
  number       = {4},
  pages        = {409--430},
  title        = {Fischer decomposition in symplectic harmonic analysis},
  url          = {http://dx.doi.org/10.1007/s10455-014-9431-3},
  volume       = {46},
  year         = {2014},
}

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