REPSN

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.


References in zbMATH (referenced in 19 articles )

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  1. Barthel, Tobias (ed.); Krause, Henning (ed.); Stojanoska, Vesna (ed.): Mini-workshop: chromatic phenomena and duality in homotopy theory and representation theory. Abstracts from the mini-workshop held March 4--10, 2018 (2018)
  2. Daubechies, Ingrid (ed.); Kutyniok, Gitta (ed.); Rauhut, Holger (ed.); Strohmer, Thomas (ed.): Applied harmonic analysis and data processing. Abstracts from the workshop held March 25--31, 2018 (2018)
  3. Denham, Graham (ed.); Gaiffi, Giovanni (ed.); Jímenez Rolland, Rita (ed.); Suciu, Alexander I. (ed.): Topology of arrangements and representation stability. Abstracts from the workshop held January 14--20, 2018 (2018)
  4. Dolzmann, Georg (ed.); Garroni, Adriana (ed.); Hackl, Klaus (ed.); Ortiz, Michael (ed.): Variational methods for the modelling of inelastic solids. Abstracts from the workshop held February 4--10, 2018 (2018)
  5. Feragen, Aasa (ed.); Hotz, Thomas (ed.); Huckemann, Stephan (ed.); Miller, Ezra (ed.): Statistics for data with geometric structure. Abstracts from the workshop held January 21--27, 2018 (2018)
  6. Rehman, Mutti-Ur; Anwar, M. Fazeel: Computing (\mu)-values for representations of symmetric groups in engineering systems (2018)
  7. Swinarski, David: Equations of Riemann surfaces with automorphisms (2018)
  8. Kulkarni, Ravindra S.: Algorithmic construction of representations of a finite solvable group. (2015)
  9. Böckle, Gebhard: Cohomological theory of crystals over function fields and applications (2014)
  10. Ulmer, Douglas: Curves and Jacobians over function fields (2014)
  11. Fischer, Maximilian; Ratz, Michael; Torrado, Jesús; Vaudrevange, Patrick K. S.: Classification of symmetric toroidal orbifolds (2013)
  12. Holthausen, Martin; Schmidt, Michael A.: Natural vacuum alignment from group theory: the minimal case (2012)
  13. Dabbaghian, Vahid; Dixon, John D.: Computing matrix representations. (2010)
  14. Dabbaghian-Abdoly, Vahid: Constructing representations of higher degrees of finite simple groups and covers. (2007)
  15. Dabbaghian-Abdoly, Vahid: Characters of some finite groups of Lie type with a restriction containing a linear character once. (2007)
  16. Dabbaghian-Abdoly, Vahid: Constructing representations of the finite symplectic group (\textSp(4,q)). (2006)
  17. Goodman, Frederick M.; Hauschild, Holly: Affine Birman-Wenzl-Murakami algebras and tangles in the solid torus (2006)
  18. Dabbaghian-Abdoly, Vahid: An algorithm for constructing representations of finite groups. (2005)
  19. Beth, Thomas: On the computational complexity of the general discrete Fourier transform (1987)