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.


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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