Branching to Levi Subgroups in Sage
In the Sage computer package, there useful exist tools for branching representations of a simple Lie group to a Levi subgroup. See for example the root system branchingRules⊆ combinatorics in the Sage manual
Explicitly, one is branching to subgroup corresponding to a Dynkin sub-diagram, obtained by removing a single node.
For example, we can branch from SL(n) to the subgroup SL(n−1). However, SL(n−1) can be considered as "living" in the larger subgroup SL(n−1)×U(1). This is true for every subgroup coming from a deleted node, i.e. one can always take the product of the subgroup with U(1), to obtain a larger subgroup.
How does one branch to this subgroup in Sage. For example, it is done in the LieArt program for mathematica: see A3 of the ArXiv version of Lie Art.
Is this also possible in Sage?