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We study certain ${\mathfrak s}{\mathfrak l}(2,{\mathbb C})$-actionsassociated to specific examples of branching of scalar generalized Vermamodules for compatible pairs $({\mathfrak g},{\mathfrak p})$, $({\mathfrakg}',{\mathfrak p}')$ of Lie algebras and their parabolic subalgebras.

Branching problems and ${\mathfrak s}{\mathfrak l}(2,{\mathbb C})$-actions