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Structure of the kernel of higher spin Dirac operators. (English) Zbl 1090.53502

Polynomials on \(\mathbb R^n\) with values in an irreducible \(\text{Spin}_n\)-module form a natural representation space for the group \(\text{Spin}_n\) that is completely reducible. The author deduces a complete description of the decomposition into irreducible components 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 \(\mathbb R^n\) with values in these modules. Special attention is paid to the relations to higher spin Dirac operators and the Littlewood-Richardson rule.

MSC:

53A30 Conformal differential geometry (MSC2010)
53A55 Differential invariants (local theory), geometric objects
32A50 Harmonic analysis of several complex variables
43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
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