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

Fred Brackx UGent, Hennie De Schepper UGent, David Eelbode, Roman Lávička and Vladimir Souček (2016) MATHEMATICAL METHODS IN THE APPLIED SCIENCES . 39(16). p.4874-4891
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Fischer decomposition, quaternionic monogenicity
journal title
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Math. Meth. Appl. Sci.
volume
39
issue
16
pages
4874 - 4891
publisher
Wiley-Blackwell
place of publication
111 RIVER ST, HOBOKEN 07030-5774, NJ USA
Web of Science type
Article
Web of Science id
000385719500020
JCR category
MATHEMATICS, APPLIED
JCR impact factor
1.017 (2016)
JCR rank
108/255 (2016)
JCR quartile
2 (2016)
ISSN
0170-4214
1099-1476
DOI
10.1002/mma.3910
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
8502637
handle
http://hdl.handle.net/1854/LU-8502637
date created
2017-01-17 14:58:01
date last changed
2017-01-19 09:11:14
@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},
}

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.