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A Constructive Proof of Brauer's Theorem on Induced Characters in the Group Ring

Published online by Cambridge University Press:  18 December 2013

Fedor Bogomolov  and
Frederick P. Greenleaf
Fedor Bogomolov
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA (bogomolo@cims.nyu.edu)
Frederick P. Greenleaf
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA (bogomolo@cims.nyu.edu)
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Abstract

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We provide an alternative constructive proof of the classical Brauer theorem for finite groups based on the well-known description of the complex irreducible representations of the symmetric groups Sn. The theorem is first proved for Sn and then for general G by embedding in Sn and applying the Mackey subgroup theorem.

Keywords

Brauer theoremsymmetric groupslong cyclesinduced charactersYoung diagramsPrimary 20B3020C1520C30Secondary 06B15
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 31 - 53
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Boltje, R., A canonical Brauer induction formula, in Représentations linéaires des groupes finis, Luminy, 16–21 mai 1988 (Society de Mathématiques de France, Paris, 1990).Google Scholar
2.Brauer, R., On Artin's L-series with general group characters, Annals Math. 48(2) (1947), 505–514.Google Scholar
3.Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, American Mathematical Society Chelsea Publishing Series, Volume 356 (American Mathematical Society, Providence, RI, 2006).Google Scholar
4.Fulton, W. and Harris, J., Representation theory: a first course, Graduate Texts in Mathematics, Volume 129 (Springer, 1991).Google Scholar
5.Hall, M. Jr, The theory of groups, American Mathematical Society Chelsea Publishing Series, Volume 288 (American Mathematical Society, Providence, RI, 1976).Google Scholar
6.Mackey, G. W., On induced representations of groups, Am. J. Math. 73 (1951), 576–592.Google Scholar
7.Mackey, G. W., The theory of unitary group representations, Chicago Lectures in Mathematics Series (University of Chicago Press, 1976).Google Scholar
8.Serre, J.-P., Linear representations of finite groups, Graduate Texts in Mathematics, Volume 42 (Springer, 1977).CrossRefGoogle Scholar
9.Snaith, V., Explicit Brauer induction, Invent. Math. 94(3) (1988), 455–478.CrossRefGoogle Scholar