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### 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 $branching Rules \subseteq$ 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 $SL(n-1) \times U1$. This is true for every subgroup coming from a deleted node, i.e. one can always take the product of the subgroup with U1, 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? 2 None

### 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 $branching Rules \subseteq$ 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 $SL(n-1) \times U1$. This is true for every subgroup coming from a deleted node, i.e. one can always take the product of the subgroup with U1, 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? 3 None

### Branching to Levi Subgroups in SAGESage

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?