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

## Pavle Pandžić and Petr Somberg

Address:

P. Pandžić, Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

P. Somberg, Mathematical Institute of Charles University, Sokolovská 83, 18000 Praha 8, Czech Republic

E-mail:

pandzic@gmail.com

somberg@karlin.mff.cuni.cz

Abstract: 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.

AMSclassification: primary 22E47.

Keywords: representation theory of simple Lie algebra, generalized Verma modules, singular vectors and composition series, relative Lie algebra and Dirac cohomology.

DOI: 10.5817/AM2015-5-331