Automating symmetry-breaking calculations
P. C. Matthews
Abstract: The process of classifying possible symmetry-breaking bifurcations
requires a computation involving the subgroups and irreducible
representations of the original symmetry group. It is
shown how this calculation can be automated using a group theory
package such as GAP. This enables a
number of new results to be obtained for larger symmetry groups,
where manual computation is impractical. Examples of symmetric
and alternating groups are given, and the method is also applied
to the spatial symmetry-breaking of periodic patterns observed in
experiments.
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