Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T09:36:56.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Imprimitive, Irreducible Complex Characters of the Alternating Group

Published online by Cambridge University Press:  20 November 2018

Dragomir Ž. Djoković  and
Jerry Malzan
Dragomir Ž. Djoković
Affiliation:
University of Waterloo, Waterloo, Ontario
Jerry Malzan
Affiliation:
University of Waterloo, Waterloo, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to list all of the characters of An, the alternating group, mentioned in the title. The same problem for the symmetric group, Sn, was dealt with by the authors in [1]. We showr here that, apart from a few exceptions, the imprimitive, irreducible complex characters of An fall naturally into two infinite families. (Throughout this paper characters are taken over the complex numbers.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1199 - 1204
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Djokovic, D. Z. and Malzan, J., Imprimitive, irreducible complex characters of the symmetric group, Math. Z. 188 (1974), 219–224.Google Scholar
2. Jordan, C., Recherches sur les substitutions, J. Math. Pures et Appliquées, ser. 2, 17 (1872), 351–367.Google Scholar
3. Kerber, A., Representations of permutation groups I, Springer-Verlag, Lecture Notes in Mathematics 21fi (New York 1971).Google Scholar
4. Littlew∞d, D. E., The characters and representations of imprimitive groups, Proc. London Math. Soc. (3) 6 (1956), 251–266.Google Scholar
5. Littlew∞d, D. E., Group characters and the structure of groups, Proc. London Math. Soc. 39 (1935), 150–199.Google Scholar
6. Manning, W. A., The primitive groups of class 2p which contain a substitution of order p and degree 2p, Trans. Amer. Math. Soc. 4 (1903), 351–357.Google Scholar
7. Miller, G. A., On the primitive groups of class four, Amer. Math. Monthly 9 (1902), 63–66.Google Scholar
8. de, G. Robinson, B., Representation theory of the symmetric group (University of Toronto Press, 1961).Google Scholar
9. Serre, J.-P., Representations linéaires des groupes finis (Hermann, Paris 1967).Google Scholar