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Dunkl operators and a family of realizations of sop(1|2)

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Abstract
In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1 vertical bar 2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects of this operator are studied, such as the associated measure, the related Laguerre polynomials and the related Fourier transform. For special values of the parameters, it is possible to construct the kernel of the Fourier transform explicitly, as well as the related intertwining operator.
Keywords
REPRESENTATION, REFLECTION GROUPS, POLYNOMIALS, Dunkl operators, Laguerre polynomials, generalized Fourier transform, Clifford analysis, Kelvin transform

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Chicago
De Bie, Hendrik, Bernd Orsted, Petr Somberg, and Vladimir Soucek. 2012. “Dunkl Operators and a Family of Realizations of Sop(1|2).” Transactions of the American Mathematical Society 364 (7): 3875–3902.
APA
De Bie, H., Orsted, B., Somberg, P., & Soucek, V. (2012). Dunkl operators and a family of realizations of sop(1|2). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 364(7), 3875–3902.
Vancouver
1.
De Bie H, Orsted B, Somberg P, Soucek V. Dunkl operators and a family of realizations of sop(1|2). TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2012;364(7):3875–902.
MLA
De Bie, Hendrik et al. “Dunkl Operators and a Family of Realizations of Sop(1|2).” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 364.7 (2012): 3875–3902. Print.
@article{3032075,
  abstract     = {In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1 vertical bar 2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects of this operator are studied, such as the associated measure, the related Laguerre polynomials and the related Fourier transform. For special values of the parameters, it is possible to construct the kernel of the Fourier transform explicitly, as well as the related intertwining operator.},
  articleno    = {PII S 0002-9947(2012)05608-X},
  author       = {De Bie, Hendrik and Orsted, Bernd and Somberg, Petr and Soucek, Vladimir},
  issn         = {0002-9947},
  journal      = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY},
  keywords     = {REPRESENTATION,REFLECTION GROUPS,POLYNOMIALS,Dunkl operators,Laguerre polynomials,generalized Fourier transform,Clifford analysis,Kelvin transform},
  language     = {eng},
  number       = {7},
  pages        = {PII S 0002-9947(2012)05608-X:3875--PII S 0002-9947(2012)05608-X:3902},
  title        = {Dunkl operators and a family of realizations of sop(1|2)},
  volume       = {364},
  year         = {2012},
}

Web of Science
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