Branching to Levi Subgroups in Sage

asked 2019-03-06 15:10:48 -0600

nadiasusy gravatar image

updated 2019-03-07 05:51:58 -0600

slelievre gravatar image

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

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