Conformally covariant differential symmetry breaking operators for a vector bundle of rank 3 on S3

Abstract

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