Howe duality in Dunkl superspace  

作　　者：REN GuangBin 1,2 1 Department of Mathematics, University of Science and Technology of China, Hefei 230026, China 2 Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal 

出　　处：《Science China Mathematics》2010年第12期3153-3162,共10页中国科学：数学（英文版）

基　　金：supported by the Unidade de Investigao "Matemtica e Aplicaoes"of University of Aveiro;National Natural Science Foundation of China (Grant No. 10771201);support by Ghent University and expresses his sincere gratitude to Prof. F. Brackx, H. De Schepper,and F. Sommen for the kind hospitality during the visit

摘　　要：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.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.

关 键 词：Dunkl OPERATORS SUPERSPACE FISCHER DECOMPOSITION DIRAC OPERATOR 

分 类 号：O177[理学—数学]