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Computing Irreducible Representations of Finite Groups

1990
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Mathematics of Computation
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We consider the bit-complexity of the problem stated in the title. Exact computations in algebraic number fields are performed symbolically. We present a polynomial-time algorithm to find a complete set of nonequivalent irreducible representations over the field of complex numbers of a finite group given by its multiplication table. In particular, it follows that some representative of each equivalence class of irreducible representations admits a polynomial-size description. We also consider

doi:10.2307/2008443
fatcat:fqjtiyjmu5cgjkkwdbt3ha7pom