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Archiv der Mathematik

, Volume 78, Issue 6, pp 417–429 | Cite as

The character values of the irreducible constituents of a transitive permutation representation

  • G. O. Michler
  • M. Weller

Abstract.

In this article we determine the irreducible ordinary characters \( \chi_r \) of a finite group G occurring in a transitive permutation representation (1 M ) G of a given subgroup M of G, and their multiplicities \( m_r = ((1_{M})^G, \chi_r) \neq 0 \) by means of a new explicit formula calculating the coefficients a rk of the central idempotents \( e_r = \sum\limits_{k=1}^{d} a_{rk} D_k \) in the intersection algebra \( \cal B \) of (1 M ) G generated by the intersection matrices D k corresponding to the double coset decomposition \( G = \bigcup\limits_{k=1}^{d} Mx_{k} M \).¶Furthermore, an explicit formula is given for the calculation of the character values \( \chi_{r}(x) \) of each element \( x \in G \). Using this character formula we obtain a new practical algorithm for the calculation of a substantial part of the character table of G.

Keywords

Explicit Formula Finite Group Substantial Part Double Coset Character Table 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • G. O. Michler
    • 1
  • M. Weller
    • 1
  1. 1.Institute for Experimental Mathematics, University of Essen, Ellernstr. 29, 45326 Essen, Germany¶ e-mail G. O. Michler: archiv@exp-math.uni-essen.de¶ e-mail M. Weller: eowmob@exp-math.uni-essen.deDE

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