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Structure of the kernel of higher spin Dirac operators

Martin Plechšmíd — 2001

Commentationes Mathematicae Universitatis Carolinae

Polynomials on $ℝ^{n}$ with values in an irreducible ${Spin}_{n}$ -module form a natural representation space for the group ${Spin}_{n}$ . 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 $ℝ^{n}$ with values in these modules.

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