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A Generalization of the Young Diagram

Published online by Cambridge University Press:  20 November 2018

M. D. Burrow
M. D. Burrow*
Affiliation:
McGill University
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The method of A. Young for finding the set of primitive idempotents of the group algebra of the symmetric group is classical; it was first given by Frobenius (4) using results of Young (10 and 11). A concise account can be found in (9) and a very detailed treatment in (6).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 498 - 508
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Artin, E., Nesbitt, C. J. and Thrall, R. M., Rings with minimum condition (U. of Mich. Press, 1948).Google Scholar
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3. Frame, J. S., An irreducible representation extracted from two permutation groups, Ann. Math., 55 (1952), 85–100.Google Scholar
4. Frobenius, G., Ueber die characterischen Einheiten der symmetrischen Gruppe, Sitz. Preuss. Akad. (1903), I, 328–358.Google Scholar
5. Littlewood, D. E., Group representations (2nd ed.).Google Scholar
6. Rutherford, D. E., Substitutional analysis (Edinburgh, 1948).Google Scholar
7. Steinberg, R., The representations of GL(3, q), GL(4, q), PGL(3, q) and PGL(4, q), Can. J. Math., 3 (1951), 225–235.Google Scholar
8. Steinberg, R., A geometric approach to the representations of the full linear group over a Galois field, Trans. Amer. Math. Soc, 71 (1951), 274–282.Google Scholar
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10. Young, A., On quantitative substitutional analysis, Proc. London Math. Soc, 83 (1900), 97–146.Google Scholar
11. Young, A., On quantitative substitutional analysis, Proc. London Math. Soc, 34 (1902), 361–397.Google Scholar