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- Title
Hermitian generalization of the Rarita-Schwinger operators.
- Authors
Damiano, Alberto; Eelbode, David
- Abstract
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 $$ \partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} } $$ and $$ \partial _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{z} }^\dag $$ 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.
- Subjects
HERMITIAN forms; DIFFERENTIAL operators; DIFFERENTIAL equations; OPERATOR theory; FUNCTIONAL analysis
- Publication
Acta Mathematica Sinica, 2010, Vol 26, Issue 2, p311
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-010-7672-z