Computing irreducible representations of finite groups

László Babai, Lajosr Ronyai

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

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 '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 'V is given by the list of matrices (^(g) ', g 6 G); and in randomized (Las Vegas) polynomial time under the more concise input ('P'(g); g € S), where S is a set of generators of G.

Original languageEnglish
Pages (from-to)705-722
Number of pages18
JournalMathematics of Computation
Volume55
Issue number192
DOIs
Publication statusPublished - Oct 1990

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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