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Irreducible representations of the generalized symmetric group Bmn

Published online by Cambridge University Press:  18 May 2009

M. Saeed-ul-Islam
M. Saeed-ul-Islam
Affiliation:
Department of Pure Mathematics, University College Of Wales, Aberystwyth, U.K.
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This paper is devoted to the determining of the irreducible linear representations of the generalized symmetric group (elsewhere written as , Cm ≀ Sn or G(m, 1, n)) by considering the conjugacy classes of and then constructing the same number of inequivalent irreducible linear representations of . These have previously been determined by Kerber [2, Section 5] using Clifford's theory applied to wreath products.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 1 - 6
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Coxeter, H. S. M., The abstract groups , and , Proc. London Math. Soc. 41 (1936), 278–301.CrossRefGoogle Scholar
2.Kerber, A., Representations of Permutations Groups I, Lecture Notes in Mathematics, No. 240 (Springer, 1971).CrossRefGoogle Scholar
3.Osima, M., On the representations of the generalized symmetric groups, Math. J. Okayama Univ. 4 (1954), 39–56.Google Scholar
4.Puttaswamaiah, B. M., Unitary representations of generalized symmetric groups, Canad. J. Math. 21 (1969), 28–38.CrossRefGoogle Scholar
5.Read, E. W., On the α-regular classes of the generalised symmetric group, Glasgow Math. J. 17 (1976), 144–150.CrossRefGoogle Scholar
6.Saeed-ul-Islam, M., Irreducible projective representations of the generalized symmetric group , Proc. XII international Colloq. on Group Theoretical Methods in Physics, Lecture Notes in Physics No. 201 (Springer, 1983), 70–72.Google Scholar