ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 06 Mar 2019 15:10:48 -0600Branching to Levi Subgroups in Sagehttp://ask.sagemath.org/question/45691/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 $\operatorname{SL}(n)$ 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?Wed, 06 Mar 2019 15:10:48 -0600http://ask.sagemath.org/question/45691/branching-to-levi-subgroups-in-sage/