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On the Reduction of Permutation Representations

Published online by Cambridge University Press:  20 November 2018

B. M. Puttaswamaiah
B. M. Puttaswamaiah*
Affiliation:
University of Toronto and University of Mysore
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In this paper an attempt is made to generalize the rather special role played by certain "Young subgroups" of Sn. In Theorem 1, the substitutional equation involving Young's raising operators for Sn is generalized to apply to an arbitrary subgroup H of a finite group G. Applying this to Sn, it is shown how the multiplicities mλH can be calculated in terms of the raising operators in Theorem 2, which calculations are illustrated by a simple example.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 6 , Issue 3 , 01 September 1963 , pp. 385 - 395
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Brauer, R., A characterization of characters of finite groups, Annals of Mathematics, Vol. 57, No. 2, (1953).Google Scholar
2. Prokop, W., Thesis, Eidgenőssische Technische Hochscule, Zurich (1948).Google Scholar
3. de B. Robinson, G., The Representation Theory of the Symmetric Group, University of Toronto Press (1961).Google Scholar