Displaying similar documents to “BGG sequences on spheres”

Structure of the kernel of higher spin Dirac operators

Martin Plechšmíd (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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. ...

Twistor operators on conformally flat spaces

Somberg, Petr

Similarity:

Summary: We describe explicitly the kernels of higher spin twistor operators on standard even dimensional Euclidean space ℛ 2 l , standard even dimensional sphere S 2 l , and standard even dimensional hyperbolic space ℋ 2 l , using realizations of invariant differential operators inside spinor valued differential forms. The kernels are finite dimensional vector spaces (of the same cardinality) generated by spinor valued polynomials on ℛ 2 l , S 2 l , ℋ 2 l .