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On p-quotients and star diagrams of the symmetric group

Published online by Cambridge University Press:  24 October 2008

H. Farahat
H. Farahat
Affiliation:
University College of North WalesBangor
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Extract

The star diagram of a diagram [λ] was first obtained by Robinson (5) who denned and studied it, thus giving a unique characterization of the hook structure of [λ]. Staal (6) continued Robinson's work and obtained some important results. Recently, Littlewood (2) published a paper on the modular representations of the symmetric group in which he defined ‘congruent partitions’, ‘p-quotients’, etc., relating to the diagram [λ]. Littlewood's ideas, though superficially different from those of Robinson and Staal, are in essence equivalent to them.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 157 - 160
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Brauer, R. and Robinson, G. de B.On a conjecture by Nakayama. Trans. roy. Soc. Can. (3), 41/iii (1947), 11.Google Scholar
(2)Littlewood, D. E.Modular representations of symmetric groups. Proc. roy. Soc. A, 209 (1951), 333.Google Scholar
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(5)Robinson, G. de B.On the representations of the symmetric group, III. Amer. J. Math. 70 (1948), 277.CrossRefGoogle Scholar
(6)Staal, R. A.Star diagrams and the symmetric group. Can. J. Math. 2 (1950), 79.CrossRefGoogle Scholar