Geodesic
Structure of the kernel of higher spin Dirac operators
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 665-680

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Polynomials on $\Bbb R^n$ with values in an irreducible $\operatorname{Spin}_n$-module form a natural representation space for the group $\operatorname{Spin}_n$. These representations are completely reducible. In the paper, we give a complete description of their decompositions into irreducible components for polynomials with values in a certain range of irreducible modules. The results are used to describe the structure of kernels of conformally invariant elliptic first order systems acting on maps on $\Bbb R^n$ with values in these modules.
Classification : 32A50, 43A65, 53A30, 53A55, 53C27
Keywords: conformally invariant differential operators; generalized (higher-spin) Dirac operators; representations of spin-groups; Littlewood-Richardson rule 
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     author = {Plech\v{s}m{\'\i}d, Martin},
     title = {Structure of the kernel of higher spin {Dirac} operators},
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     zbl = {1090.53502},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a7/}
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Plechšmíd, Martin. Structure of the kernel of higher spin Dirac operators. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 4, pp. 665-680. http://geodesic.mathdoc.fr/item/CMUC_2001__42_4_a7/