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conformally invariant differential operators; generalized (higher-spin) Dirac operators; representations of spin-groups; Littlewood-Richardson rule
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.
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