Computing matrix representations. Let G be a finite group and χ a faithful irreducible character for G. Earlier papers by the first author describe techniques for computing a matrix representation for G which affords χ whenever the degree χ(1) is less than 32. In the present paper we introduce a new, fast method which can be applied in the important case where G is perfect and the socle soc(G/Z(G)) of G over its centre is Abelian. In particular, this enables us to extend the general construction of representations to all cases where χ(1)≤100. The improved algorithms have been implemented in the new version 3.0.1 of the GAP package REPSN by the first author.

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  1. Rehman, Mutti-Ur; Anwar, M. Fazeel: Computing (\mu)-values for representations of symmetric groups in engineering systems (2018)
  2. Swinarski, David: Equations of Riemann surfaces with automorphisms (2018)
  3. Kulkarni, Ravindra S.: Algorithmic construction of representations of a finite solvable group. (2015)
  4. Böckle, Gebhard: Cohomological theory of crystals over function fields and applications (2014)
  5. Ulmer, Douglas: Curves and Jacobians over function fields (2014)
  6. Fischer, Maximilian; Ratz, Michael; Torrado, Jesús; Vaudrevange, Patrick K. S.: Classification of symmetric toroidal orbifolds (2013)
  7. Holthausen, Martin; Schmidt, Michael A.: Natural vacuum alignment from group theory: the minimal case (2012)
  8. Dabbaghian, Vahid; Dixon, John D.: Computing matrix representations. (2010)
  9. Dabbaghian-Abdoly, Vahid: Constructing representations of higher degrees of finite simple groups and covers. (2007)
  10. Dabbaghian-Abdoly, Vahid: Characters of some finite groups of Lie type with a restriction containing a linear character once. (2007)
  11. Dabbaghian-Abdoly, Vahid: Constructing representations of the finite symplectic group (\textSp(4,q)). (2006)
  12. Goodman, Frederick M.; Hauschild, Holly: Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus (2006)
  13. Dabbaghian-Abdoly, Vahid: An algorithm for constructing representations of finite groups. (2005)
  14. Beth, Thomas: On the computational complexity of the general discrete Fourier transform (1987)