Restrictions of Verma Modules to Symmetric Pairs and Some Applications to Differential Geometry. Workshop on the Interaction of Representation Theory with Geometry and Combinatorics. Hausdorff Institute, Bonn, Germany, 28 March-1 April 2011.

I will discuss a ''framework'' of branching problems for generalized Verma modules with respect to reductive symmetric pairs from the viewpoint of ''discrete decomposability'', and explain some basic results on the size of irreducible summands and multiplicities.

As an application, I plan to explain a new and simple method to obtain Rankin-Cohen operators for holomorphic automorphic forms and Juhl's conformally equivariant differential operators together with their generalizations.

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