Hermitian Generalization of the Rarita-Schwinger Operators

作     者：Alberto DAMIANO David EELBODE 

作者机构：Mathematics Institute of Charles University Department of Mathematics and Computer Science University of Antwerp 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2010年第26卷第2期

页      面：311-330页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：sponsored by the relevant grants supported by the F.W.O. Vlaanderen (Belgium) 

主　　题：Hermitian Clifford analysis Rarita-Schwinger operator 

摘      要：We introduce two new linear differential operators which are invariant with respect to the unitary group SU（n）. They constitute analogues of the twistor and the Rarita-Schwinger operator in the orthogonal case. The natural setting for doing this is Hermitian Clifford Analysis. Such operators are constructed by twisting the two versions of the Hermitian Dirac operator 6z_ and 6z_ and then projecting on irreducible modules for the unitary group. We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita-Schwinger operators in terms of Hermitian monogenic polynomials.