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

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  • H. de Bie, Ghent University
  • ,
  • B. Ørsted
  • P. Somberg, Mathematical Institute of Charles University
  • ,
  • V. Souček, Mathematical Institute of Charles University
In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|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.
Original languageEnglish
JournalTransactions of the American Mathematical Society
Volume364
Issue7
Pages (from-to)3875-3902
Number of pages28
ISSN0002-9947
DOIs
Publication statusPublished - 2012

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