Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 over S^3

Abstract

We construct and give a complete classification of all the differential symmetry breaking operators D_{λ,ν}^m : C^\infty(S^3, V^3_λ) \rightarrow C^\infty(S^2,L_{m,ν}), between the spaces of smooth sections of a vector bundle of rank 3 over the 3-sphere V^3_λ \rightarrow S^3, and a line bundle over the 2-sphere L_{m,ν} \rightarrow S^2. In particular, we give necessary and sufficient conditions on the tuple of parameters (λ, ν, m) for which these operators exist.