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.

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© Toshiyuki Kobayashi