Science China Mathematics

, Volume 53, Issue 12, pp 3153–3162 | Cite as

Howe duality in Dunkl superspace

Articles

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.

Keywords

Dunkl operators superspace Fischer decomposition Dirac operator 

MSC(2000)

Primary 30G35 Secondary 31A30 33C52 58C50 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Department of MathematicsUniversity of AveiroAveiroPortugal

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