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The Inner Plethysm of S-Functions

Published online by Cambridge University Press:  20 November 2018

D. E. Littlewood
D. E. Littlewood*
Affiliation:
University College of North Wales,Bangor
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In a previous paper (2), the inner product of two S-functions {λ}.{μ} was defined for (λ),(μ) partitions of the same integer n. Briefly, the ordinary product {λ}.{μ} of two S-functions corresponds to the analysis of the direct product of two corresponding representations of the full linear group, while the inner product {λ}.{μ} corresponds to the analysis of the direct product of two representations of the corresponding symmetric group.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 1 - 16
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Littlewood, D. E., The theory of group characters and matrix representations of groups (2nd ed., Oxford, 1950).Google Scholar
2. Littlewood, D. E., The Kronecker product of symmetric group representations, J. London Math. Soc, 81 (1956), 89–93.Google Scholar
3. Littlewood, D. E., The characters and representations of imprimitive groups, Proc. London Math. Soc, (3) 6 (1956), 251–266.Google Scholar
4. Littlewood, D. E., Plethysm and the inner product of S-functions, J. London Math. Soc, 32 (1957), 18–22.Google Scholar
5. Murnaghan, F. D., On the generation of irreducible representations of the symmetric group, Proc Nat. Acad. Sci., U.S.A., 41 (1955), 514–515.Google Scholar
6. Robinson, G. de B., On the representations of the symmetric group, III. Amer. J. Math. 70 (1948), 277–294.Google Scholar