Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-28T10:03:11.025Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
(3)Nakayama, T.On some modular properties of irreducible representations of symmetric groups, I and II. Jap. J. Math. 17 (1941), 165, 411.CrossRefGoogle Scholar
(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