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Keywords:
representation theory of simple Lie algebra; generalized Verma modules; singular vectors and composition series; relative Lie algebra and Dirac cohomology
representation theory of simple Lie algebra; generalized Verma modules; singular vectors and composition series; relative Lie algebra and Dirac cohomology
Summary:
We study certain ${\mathfrak{sl}}(2,\mathbb{C})$-actions associated to specific examples of branching of scalar generalized Verma modules for compatible pairs $(\mathfrak{g},\mathfrak{p})$, $(\mathfrak{g}^{\prime },\mathfrak{p}^{\prime })$ of Lie algebras and their parabolic subalgebras.
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