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Differential symmetry breaking operators. II: Rankin-Cohen operators for symmetric pairs. (English) Zbl 1342.22029
In this second part of their study of differential symmetry breaking operators, the authors obtain new explicit formulae describing differential symmetry breaking operators for the six different complex geometries arising from semi-simple symmetric pairs of split rank one. It is explained why coefficients of orthogonal polynomials appear in three of the cases and why normal derivatives are symmetry breaking operators in the remaining three cases. The authors also study the problem of branching for Verma modules and explain the unconventional behavior of branching multiplicities at singular values of parameters.
For Part I see [the authors, ibid. 22, No. 2, 801-845 (2016; Zbl 1338.22006)].

##### MSC:
 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) 22E46 Semisimple Lie groups and their representations 11F55 Other groups and their modular and automorphic forms (several variables) 53C10 $$G$$-structures
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