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Induced Representations and Invariants

Published online by Cambridge University Press:  20 November 2018

G. DE B. Robinson
G. DE B. Robinson*
Affiliation:
The University of Toronto
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1. Introduction. The problem of the expression of an invariant matrix of an invariant matrix as a direct sum of invariant matrices is intimately associated with the representation theory of the full linear group on the one hand and with the representation theory of the symmetric group on the other. In a previous paper the author gave an explicit formula for this reduction in terms of characters of the symmetric group. Later J. A. Todd derived the same formula using Schur functions, i.e. characters of representations of the full linear group.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 334 - 343
Copyright
Copyright © Canadian Mathematical Society 1950

References

[1] Littlewood, D. E., Invariant Theory, Tensors and Group Characters, Phil. Trans. Roy. Soc. (A), vol. 239 (1944), 305–365.Google Scholar
[2] Littlewood, D. E., Invariants of Systems of Quadrics, Proc. London Math. Soc., vol. 49 (1947), 289–306.Google Scholar
[3] Robinson, G. de B., On the Representations of the Symmetric Group, Second Paper, Amer. J. Math., vol. 69 (1947), 286–298.Google Scholar
[4] Robinson, G. de B., Third Paper, ibid., vol. 70 (1948), 277–294.Google Scholar
[5] Robinson, G. de B., On the Disjoint Product of Irreducible Representations of the Symmetric Group, Can. J. Math., vol. 1 (1949), 166–175.Google Scholar
[6] Staal, R. A., Star Diagrams and the Symmetric Group, Can. J. Math., vol. 2 (1950), 79–92.Google Scholar
[7] Todd, J. A., A Note on the Algebra of S-functions, Proc. Cambridge Phil. Soc., vol. 45 (1949), 328–334.Google Scholar
[8] Todd, J. A., N0te on a Paper by Robinson, Can. J. Math., vol. 2 (1950), 331–333.Google Scholar