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Algorithm to check is representation irreducuble irreducible ? Algorithm to decompose the reducible one ? |
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Algorithm to check is representation irreducuble ? Algorithm to decompose the reducible one ?Question 1 Given a representation of a finite group, what algorithm can be used to check is it irreducible or not ? (Main case - complex numbers, comments on other cases are also welcome. "Given" means finite set of matrices is given). Question 2 Given a representation of a finite group, what algorithms can be used to decompose it to the direct sum of irreducibles) ? For the question 1 I would do the following: rep is irrep if its commutant consists of scalar matrices. So I can try to find matrices commuting with all elements of the group and look whether I get only scalar matrices. Are there more effective ways to do it ? Related question: http://mathoverflow.net/questions/111379/how-to-compute-all-irreducible-representations-of-a-finite-group-how-gap-is-do
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