Computing Irreducible Representations of Groups
نویسنده
چکیده
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 ( á 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.
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