Hostname: page-component-84b7d79bbc-g78kv Total loading time: 0 Render date: 2024-07-30T11:16:42.298Z Has data issue: false hasContentIssue false
  • English
  • Français

On tensor factorisation for representations of finite groups

Published online by Cambridge University Press:  17 April 2009

Emanuele Pacifici
Emanuele Pacifici
Affiliation:
Dipartimento di Matematica ‘Ulisse Dini’, Università degli Studi di Firenze, viale Morgagni 67-A, 50134 Firenze, Italy, e-mail: pacifici@math.unifi.it
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.

We prove that, given a quasi-primitive complex representation D for a finite group G, the possible ways of decomposing D as an inner tensor product of two projective representations of G are parametrised in terms of the group structure of G. More explicitly, we construct a bijection between the set of such decompositions and a particular interval in the lattice of normal subgroups of G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 161 - 171
Copyright
Copyright © Australian Mathematical Society 2004

References

[1] Curtis, C.W. and Reiner, I., Methods of representation theory I (J. Wiley and Son, New York, 1981).Google Scholar
[2] Dixon, J.D., The structure of linear groups (Van Nostrand Reinhold, London, 1971).Google Scholar
[3] Ferguson, P.A. and Turull, A., ‘Prime characters and factorizations of quasi-primitive characters’, Math. Z. 190 1985, 583–604.CrossRefGoogle Scholar
[4] Gajendragadkar, D., ‘A characteristic class of characters of finite π-separable groups’, J. Algebra 59 1979, 237–259.CrossRefGoogle Scholar
[5] Gorenstein, D., Finite groups (Harper & Row, New York, 1968).Google Scholar
[6] Huppert, B., Character theory of finite groups (De Gruyter, Berlin, 1998).CrossRefGoogle Scholar
[7] Isaacs, I.M., Character theory of finite groups (Academic Press, New York, 1976).Google Scholar
[8] Isaacs, I.M., ‘Primitive characters, normal subgroups and M-Groups’, Math. Z. 177 1981, 267–284.CrossRefGoogle Scholar
[9] Kovács, L.G., ‘On tensor induction of group representations’, J. Aust. Math. Soc. Ser. A 49 1990, 486–501.CrossRefGoogle Scholar