## *Homomorphisms between Verma Modules and Symmetry Breaking
Operators* (opening lecture).
Representation
Theory of Reductive Lie Groups and Algebras: in honor of Hisayosi
Matumoto on the occasion of his 60th birthday. the University of Tokyo,
Japan, 27-29 March 2019.

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