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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Computing irreducible representations of finite groups
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by László Babai and Lajos Rónyai PDF
Math. Comp. 55 (1990), 705-722 Request permission


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 the problem of decomposing a given representation $\mathcal {V}$ of the finite group G over an algebraic number field F into absolutely irreducible constituents. We are able to do this in deterministic polynomial time if $\mathcal {V}$ is given by the list of matrices $\{ \mathcal {V}(g);g \in G\}$; and in randomized (Las Vegas) polynomial time under the more concise input $\{ \mathcal {V}(g);g \in S\}$, where S is a set of generators of G.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Math. Comp. 55 (1990), 705-722
  • MSC: Primary 68Q40; Secondary 11R33, 20C40
  • DOI:
  • MathSciNet review: 1035925