Abstract
In the framework of superspace in Clifford analysis for the Dunkl version, the Fischer decomposition is established for solutions of the Dunkl super Dirac operators. The result is general without restrictions on multiplicity functions or on super dimensions. The Fischer decomposition provides a module for the Howe dual pair G × osp(1|2) on the space of spinor valued polynomials with G the Coxeter group, while the generators of the Lie superspace reveal the naturality of the Fischer decomposition.
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Ren, G. Howe duality in Dunkl superspace. Sci. China Math. 53, 3153–3162 (2010). https://doi.org/10.1007/s11425-010-4063-y
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DOI: https://doi.org/10.1007/s11425-010-4063-y