### Branching to Levi Subgroups in ~~SAGE~~Sage

In the ~~SAGE ~~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 $branching Rules \subseteq $ combinatorics in the ~~SAGE ~~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 ~~$SL(n)$ ~~$\operatorname{SL}(n)$ to the subgroup ~~$SL(n-1)$. ~~$\operatorname{SL}(n-1)$.
However, ~~$SL(n-1)$ ~~$\operatorname{SL}(n-1)$ can be considered as "living" in the larger subgroup
~~$SL(n-1) ~~$\operatorname{SL}(n-1) \times ~~U1$. ~~\operatorname{U}(1)$. This is true for every subgroup coming from a deleted node, i.e. one can always take the product of the subgroup with ~~U1, ~~$\operatorname{U}(1)$, to obtain a larger subgroup.

How does one branch to this subgroup in ~~SAGE. ~~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?~~Sage?