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In the talk of Meinolf Geck at the SFB retreat he presented a decomposition helper function:
Bildschirmfoto vom 2025-03-31 09-35-50
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 to scalar_product(a*b,c), maybe this can also be used for some tests. Perhaps we could even incorporate this into the book example.

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codecov bot commented Mar 31, 2025

Codecov Report

Attention: Patch coverage is 0% with 12 lines in your changes missing coverage. Please review.

Project coverage is 93.72%. Comparing base (4d4dcc0) to head (f02e63b).
Report is 1 commits behind head on master.

Files with missing lines Patch % Lines
src/GenericCharacter.jl 0.00% 12 Missing ⚠️
Additional details and impacted files
@@            Coverage Diff             @@
##           master     #285      +/-   ##
==========================================
- Coverage   94.91%   93.72%   -1.19%     
==========================================
  Files          13       13              
  Lines         905      925      +20     
==========================================
+ Hits          859      867       +8     
- Misses         46       58      +12     

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