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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing irreducible representations of groups
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by John D. Dixon PDF
Math. Comp. 24 (1970), 707-712 Request permission

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
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • 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