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Modular Representations of the Symmetric Group

Published online by Cambridge University Press:  20 November 2018

J. H. Chung
J. H. Chung*
Affiliation:
University of Toronto
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The theory of modular representations of the symmetric group was studied first by Nakayama (5, 6), and later by Thrall and Nesbitt (11) and Robinson (7, 8, 9). Nakayama built up his elaborate theory of hooks for the express purpose of studying this problem, while Robinson's extensive work on the various phases of the relationship between Young diagrams, skew diagrams and star diagrams on the one hand, and representations of the symmetric group on the other, culminating in a set of relations among the degrees of the representations, serves as a starting point for this paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 309 - 327
Copyright
Copyright © Canadian Mathematical Society 1951

References

1. Brauer, R., On representations of groups of finite order, Proc. Nat. Acad. Sa, vol. 25 (1939), 290–295.Google Scholar
2. and Nesbitt, C., On the modular character of groups, Ann. of Math., vol. 42 (1941), 556–590.Google Scholar
3. and Robinson, G. de B., On a conjecture by Nakayama, Trans. Roy. Soc. Can, (III),vol. 40 (1947), 11–25.Google Scholar
4. Littlewood, D. E. and Richardson, A. R., Group characters and algebras, Phil. Trans. Roy. Soc. Lon. (A), vol. 233 (1934), 99–141.Google Scholar
5. Nakayama, T., On some modular properties of irreducible representations of a symmetric group, Part I, Jap. J. Math., vol. 17 (1940), 165-184. 6. , Part II, ibid., vol. 17 (1941), 411–423.Google Scholar
7. Robinson, G. de B., On the representations of the symmetric group, Amer. J. Math., vol. 60 (1938), 745–760.Google Scholar
8. Robinson, G. de B., Second Paper, ibid., vol. 69 (1947), 286–298.Google Scholar
9. Robinson, G. de B., Third Paper, ibid., vol. 70 (1948), 277–294.Google Scholar
10. Staal, R. A., Star diagrams and the symmetric group,Can. J. Math., vol. 2 (1950), 79–92.Google Scholar
11. Thrall, R. M. and Nesbitt, C. J., On the modular representations of the symmetric group, Ann. of Math., vol. 43 (1942), 656–670.Google Scholar
12. Todd, J. A., A note on the algebra of S-functions, Proc. Cambridge Phil. Soc., vol. 45 (1949),328–334.Google Scholar