Computing irreducible representations of groups

Author:
John D. Dixon

Journal:
Math. Comp. **24** (1970), 707-712

MSC:
Primary 20.80; Secondary 65.00

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 . 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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0280611-6

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