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On D. E. Littlewood's Algebra of S-Functions

  • D. G. Duncan (a1)

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Several papers have been written on the “new” multiplication of S-functions since Littlewood [3, p. 206] first suggested the problem. M. Zia-ud-Din [13] calculated the case {m} ⊗ {n} for mn ≤ 12, making use of the tables of the characters of the symmetric group of degree mn. Later Thrall [10,pp. 378-382] developed explicit formulae for the cases {m} ⊗ {2},{m} ⊗ {3}, {2} ⊗ {m} (where m is any integer).

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References

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1. Duncan, D. G., Note on a formula by Todd, J. London Math. Soc, vol. 27 (1952), 235236.
2. Foulkes, H. O., Concomitants of the quintic and sextic up to degree four in the coefficients of the ground form, J. London Math. Soc, vol. 25 (1950), 205209.
3. Littlewood, D. E., The theory of group characters and matrix representations of groups (Oxford, 1950).
4. Murnaghan, F. D., The theory of group representations (Baltimore, 1938).
5. Nakayama, T., On some modular properties of irreducible representations of a symmetric group, Jap. J. Math., vol. 17 (1940), 165184.
6. Robinson, G. de B., On the representations of the symmetric group III, Amer. J. Math., vol. 70, (1948), 277294.
7. Robinson, G. de B., On the disjoint product of irreducible representations of the symmetric group, Can. J. Math., vol. 1 (1949), 166175.
8. Robinson, G. de B., Induced representations and invariants, Can. J. Math., vol. 2 (1950), 334343.
9. Staal, R. A., Star Diagrams and the symmetric group, Can. J. Math., vol. 2 (1950), 7992.
10. Thrall, R. M., On symmetrized Kronecker powers and the structure of the free Lie ring, Amer. J. Math., vol. 64 (1942), 371388.
11. Thrall, R. M. and Robinson, G. de B., Supplement to a paper of G. de B. Robinson, Amer. J. Math., vol. 73 (1951), 721724.
12. Todd, J. A., A note on the algebra of S-functions, Proc. Cambridge Phil. Soc, vol. 45 (1949), 328334.
13. Zia-ud-Din, M., Proc. Edinburgh Math. Soc, vol. 5 (1936), 4345.
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On D. E. Littlewood's Algebra of S-Functions

  • D. G. Duncan (a1)

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