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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.

Information

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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(4)Nakayama, T. and Osima, M.Note on blocks of symmetric groups. Nagoya math. J. 2 (1951), 111.CrossRefGoogle Scholar
(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