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Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis

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Abstract
Spaces of spinor-valued homogeneous polynomials, and in particular spaces of spinor-valued spherical harmonics, are decomposed in terms of irreducible representations of the symplectic group Sp(p). These Fischer decompositions involve spaces of homogeneous, so-called osp(4|2)-monogenic polynomials, the Lie super algebra osp(4|2) being the Howe dual partner to the symplectic group Sp(p). In order to obtain Sp(p)-irreducibility this new concept of osp(4|2)-monogenicity has to be introduced as a re nement of quaternionic monogenicity; it is defi ned by means of the four quaternionic Dirac operators, a scalar Euler operator E underlying the notion of symplectic harmonicity and a multiplicative Cliff ord algebra operator P underlying the decomposition of spinor space into symplectic cells. These operators E and P, and their hermitian conjugates, arise naturally when constructing the Howe dual pair osp(4|2) x Sp(p), the action of which will make the Fischer decomposition multiplicity free.
Keywords
Fischer decomposition, quaternionic monogenicity

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Chicago
Brackx, Fred, Hennie De Schepper, David Eelbode, Roman Lávička, and Vladimir Souček. 2016. “Fischer Decomposition for Osp(4|2)-monogenics in Quaternionic Clifford Analysis.” Mathematical Methods in the Applied Sciences 39 (16): 4874–4891.
APA
Brackx, Fred, De Schepper, H., Eelbode, D., Lávička, R., & Souček, V. (2016). Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis. MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 39(16), 4874–4891.
Vancouver
1.
Brackx F, De Schepper H, Eelbode D, Lávička R, Souček V. Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis. MATHEMATICAL METHODS IN THE APPLIED SCIENCES . 111 RIVER ST, HOBOKEN 07030-5774, NJ USA: Wiley-Blackwell; 2016;39(16):4874–91.
MLA
Brackx, Fred, Hennie De Schepper, David Eelbode, et al. “Fischer Decomposition for Osp(4|2)-monogenics in Quaternionic Clifford Analysis.” MATHEMATICAL METHODS IN THE APPLIED SCIENCES 39.16 (2016): 4874–4891. Print.
@article{8502637,
  abstract     = {Spaces of spinor-valued homogeneous polynomials, and in particular spaces of spinor-valued spherical harmonics, are decomposed in terms of irreducible representations of the symplectic group Sp(p). These Fischer decompositions involve spaces of homogeneous, so-called osp(4|2)-monogenic polynomials, the Lie super algebra osp(4|2) being the Howe dual partner to the symplectic group Sp(p). In order to obtain Sp(p)-irreducibility this new concept of osp(4|2)-monogenicity has to be introduced as a re\unmatched{000c}nement of quaternionic monogenicity; it is defi\unmatched{000c}ned by means of the four quaternionic Dirac operators, a scalar Euler operator E underlying the notion of symplectic harmonicity and a multiplicative Cliff\unmatched{000b}ord algebra operator P underlying the decomposition of spinor space into symplectic cells. These operators E and P, and their hermitian conjugates, arise naturally when constructing the Howe dual pair
osp(4|2) x\unmatched{0002} Sp(p), the action of which will make the Fischer decomposition multiplicity free.},
  author       = {Brackx, Fred and De Schepper, Hennie and Eelbode, David and L{\'a}vi\v{c}ka, Roman and Sou\v{c}ek, Vladimir},
  issn         = {0170-4214},
  journal      = {MATHEMATICAL METHODS IN THE APPLIED SCIENCES },
  keyword      = {Fischer decomposition,quaternionic monogenicity},
  language     = {eng},
  number       = {16},
  pages        = {4874--4891},
  publisher    = {Wiley-Blackwell},
  title        = {Fischer decomposition for osp(4|2)-monogenics in quaternionic Clifford analysis},
  url          = {http://dx.doi.org/10.1002/mma.3910},
  volume       = {39},
  year         = {2016},
}

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