Branching Laws and F-method for Constructing Natural Differential Operators in Parabolic Geometry. Analysis Seminar. Chalmers University of Technology and the University of Gothenburg, Sweden, 14 May 2013.

As an analogy of unitary representation without continuous spectrum (''discrete decomposable representations”), we give a geometric criterion for the property ''having non-trivial subrepresentations” in the restriction of Verma modules with respect to reductive symmetric pairs.

As its application, I discuss intertwining operators in parabolic geometry, and in particular, propose a new method (F-method) to produce naturally Juhl's conformally equivariant differential operators and Cohen-Rankin operators in holomorphic automorphic forms, together with their generalizations.

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© Toshiyuki Kobayashi