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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?

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?

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?