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

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

2009-11-24

arxiv.org/abs/0911.4725v2

Mathematics

Classical Analysis and ODEs

28 pages, some small changes, accepted in Trans. Amer. Math. Soc

Scientific paper

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.

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