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In the talk of Meinolf Geck at the SFB retreat he presented a decomposition helper function:

This PR provides a first implementation. I think we should also check if all involved character types are irreducible. As far as I understand this
character_decomposition_multiplicity(a,b,c)
should be more or less equivalent toscalar_product(a*b,c)
, maybe this can also be used for some tests. Perhaps we could even incorporate this into the book example.