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Spinor spaces in discrete Clifford analysis

Hilde De Ridder (UGent) and Tim Raeymaekers (UGent)
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Abstract
In this paper we work in the ‘split’ discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions,defined on the grid Zm, of the discrete Dirac operator ∂, involving both forward and backward differences, which factorizes the (discrete) Star-Laplacian. We show how the space Mk of discrete spherical monogenics homogeneous of degree k, is decomposable into irreducible so(m)-representations.
Keywords
Discrete Clifford analysis, Irreducible representation, Orthogonal Lie algebra, Monogenic functions

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Citation

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

Chicago
De Ridder, Hilde, and Tim Raeymaekers. 2017. “Spinor Spaces in Discrete Clifford Analysis.” Complex Analysis and Operator Theory 11 (5): 1113–1137.
APA
De Ridder, H., & Raeymaekers, T. (2017). Spinor spaces in discrete Clifford analysis. COMPLEX ANALYSIS AND OPERATOR THEORY, 11(5), 1113–1137.
Vancouver
1.
De Ridder H, Raeymaekers T. Spinor spaces in discrete Clifford analysis. COMPLEX ANALYSIS AND OPERATOR THEORY. PICASSOPLATZ 4, BASEL 4052, SWITZERLAND: SPRINGER BASEL AG; 2017;11(5):1113–37.
MLA
De Ridder, Hilde, and Tim Raeymaekers. “Spinor Spaces in Discrete Clifford Analysis.” COMPLEX ANALYSIS AND OPERATOR THEORY 11.5 (2017): 1113–1137. Print.
@article{8509385,
  abstract     = { In this paper we work in the {\textquoteleft}split{\textquoteright} discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions,de\unmatched{fb01}ned on the grid Zm, of the discrete Dirac operator \ensuremath{\partial}, involving both forward and backward differences, which factorizes the (discrete) Star-Laplacian. We show how the space Mk of discrete spherical monogenics homogeneous of degree k, is decomposable into irreducible so(m)-representations. },
  author       = {De Ridder, Hilde and Raeymaekers, Tim},
  issn         = {1661-8254},
  journal      = {COMPLEX ANALYSIS AND OPERATOR THEORY},
  keyword      = {Discrete Clifford analysis,Irreducible representation,Orthogonal Lie algebra,Monogenic functions},
  language     = {eng},
  number       = {5},
  pages        = {1113--1137},
  publisher    = {SPRINGER BASEL AG},
  title        = {Spinor spaces in discrete Clifford analysis},
  url          = {http://dx.doi.org/10.1007/s11785-017-0644-x},
  volume       = {11},
  year         = {2017},
}

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