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Computing irreducible representations of groups


Author: John D. Dixon
Journal: Math. Comp. 24 (1970), 707-712
MSC: Primary 20.80; Secondary 65.00
DOI: https://doi.org/10.1090/S0025-5718-1970-0280611-6
MathSciNet review: 0280611
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Abstract: How can you find a complete set of inequivalent irreducible (ordinary) representations of a finite group? The theory is classical but, except when the group was very small or had a rather special structure, the actual computations were prohibitive before the advent of high-speed computers; and there remain practical difficulties even for groups of relatively small orders $( \leqq 100)$. The present paper describes three techniques to help solve this problem. These are: the reduction of a reducible unitary representation into its irreducible components; the construction of a complete set of irreducible unitary representations from a single faithful representation; and the calculation of the precise values of a group character from values which have only been computed approximately.


References [Enhancements On Off] (What's this?)

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Additional Information

Keywords: Computation of group representations, computation of characters, reduction of unitary representations, irreducible components, tensor products, iterative processes, finite Fourier analysis
Article copyright: © Copyright 1970 American Mathematical Society