It is classically known that homomorphisms between Verma modules induce differential intertwining opeartors for principal series representations. We extend this observation to a more general setting of branching problems for the restriction of representations for a pair of groups, and also from local operators to non-local ones such as integral symmetry breaking operators. If time permits, we discuss explicit constructions and classification of such symmetry breaking operators in conformal geometry.
© Toshiyuki Kobayashi