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Title: Decomposition of the polynomial kernel of arbitrary higher spin Dirac operators

In a series of recent papers, we have introduced higher spin Dirac operators, which are generalisations of the classical Dirac operator. Whereas the latter acts on spinor-valued functions, the former acts on functions taking values in arbitrary irreducible half-integer highest weight representations for the spin group. In this paper, we describe how the polynomial kernel spaces of such operators decompose in irreducible representations of the spin group. We will hereby make use of results from representation theory.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematics and Computer Science, University of Antwerp, Campus Middelheim, G-Building, Middelheimlaan 1, 2020 Antwerpen (Belgium)
  2. Clifford Research Group, Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Ghent (Belgium)
  3. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281, 9000 Ghent (Belgium)
Publication Date:
OSTI Identifier:
22479538
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DECOMPOSITION; DIRAC OPERATORS; IRREDUCIBLE REPRESENTATIONS; KERNELS; MATHEMATICAL SPACE; POLYNOMIALS; SPIN