Dunkl operators and a family of realizations of $\mathfrak {osp}(1\vert 2)$
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- by H. De Bie, B. Ørsted, P. Somberg and V. Souček PDF
- Trans. Amer. Math. Soc. 364 (2012), 3875-3902 Request permission
Abstract:
In this paper, a family of radial deformations of the realization of the Lie superalgebra $\mathfrak {osp}(1|2)$ 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.References
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Additional Information
- H. De Bie
- Affiliation: Department of Mathematical Analysis, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
- MR Author ID: 820584
- ORCID: 0000-0003-3806-7836
- Email: Hendrik.DeBie@UGent.be
- B. Ørsted
- Affiliation: Department of Mathematical Sciences, University of Aarhus, Building 530, Ny Munkegade, DK 8000, Aarhus C, Denmark
- Email: orsted@imf.au.dk
- P. Somberg
- Affiliation: Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha, Czech Republic
- MR Author ID: 670515
- ORCID: 0000-0001-5450-9206
- Email: somberg@karlin.mff.cuni.cz
- V. Souček
- Affiliation: Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha, Czech Republic
- Email: soucek@karlin.mff.cuni.cz
- Received by editor(s): February 12, 2010
- Received by editor(s) in revised form: March 30, 2011
- Published electronically: February 27, 2012
- Additional Notes: The first author is a Postdoctoral Fellow of the Research Foundation - Flanders (FWO) and a Courtesy Research Associate at the University of Oregon.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 3875-3902
- MSC (2010): Primary 33C52, 30G35, 43A32
- DOI: https://doi.org/10.1090/S0002-9947-2012-05608-X
- MathSciNet review: 2901238