Bulletin of the Australian Mathematical Society
- Bulletin of the Australian Mathematical Society / Volume 69 / Issue 01 / February 2004, pp 161-171
- Copyright © Australian Mathematical Society 2004
- DOI: http://dx.doi.org/10.1017/S0004972700034365 (About DOI), Published online: 17 April 2009
Research Article
On tensor factorisation for representations of finite groups
Emanuele Pacificia1
a1 Dipartimento di Matematica ‘Ulisse Dini’, Università degli Studi di Firenze, viale Morgagni 67-A, 50134 Firenze, Italy, e-mail: pacifici@math.unifi.it
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.
(Received September 22 2003)
- [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. [OpenURL Query Data] [CrossRef] [Google Scholar]
- [4] Gajendragadkar, D., ‘A characteristic class of characters of finite π-separable groups’, J. Algebra 59 1979, 237–259. [OpenURL Query Data] [CrossRef] [MathSciNet] [Google 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). [CrossRef] [Google 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. [OpenURL Query Data] [CrossRef] [Google Scholar]
- [9] Kovács, L.G., ‘On tensor induction of group representations’, J. Aust. Math. Soc. Ser. A 49 1990, 486–501. [OpenURL Query Data] [CrossRef] [MathSciNet] [CJO Abstract] [Google Scholar]
