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

TL;DR

This paper investigates ${ m sl}(2,c)$-actions related to the branching of scalar generalized Verma modules within compatible pairs of Lie algebras and their parabolic subalgebras, revealing new algebraic structures.

Contribution

It introduces a detailed study of ${ m sl}(2,c)$-actions in the context of branching problems for scalar generalized Verma modules, expanding understanding of Lie algebra representations.

Findings

Identification of specific ${ m sl}(2,c)$-actions in branching scenarios

New algebraic structures related to Verma modules

Insights into the representation theory of Lie algebras

Abstract

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