Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T00:41:11.010Z Has data issue: false hasContentIssue false
  • English
  • Français

Plethysm of S-Functions

Published online by Cambridge University Press:  20 November 2018

A. O. Usher
A. O. Usher*
Affiliation:
Royal Holloway College (University of London), Englefield Green, Surrey
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The S-function , where is the ‘new multiplication' or plethysm of D. E. Littlewood [1], corresponds, in the sense defined below in (1), to the character afforded by a representation of the symmetric group Slm induced from a representation of the subgroup . The aim of this paper is to define the latter representation and deduce its character using a somewhat different approach from that in [3].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 440 - 445
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Littlewood, D. E., Invariant theory, tensors and group characters, Trans. Royal Phil. Soc. 239 (1944), 305–365.Google Scholar
2. Littlewood, D. E., The theory of group characters (Oxford, 1940).Google Scholar
3. Robinson, G. de B., On the disjoint product of irreducible representations of the symmetric group, Can. J. Math. 1, (1949), 166–175.Google Scholar
4. Robinson, G. de B., Representation theory of the symmetric group (Edinburgh, 1961).Google Scholar
5. Foulkes, H. O., Differential operators associated with S-functions, J. London Math. Soc. 2J+ (1949), 136–143.Google Scholar
6. Hall, M., The theory of groups (Macmillan, 1959).Google Scholar
7. Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (Wiley, 1962).Google Scholar
8. Kerber, A., Representations of permutation groups, Lecture notes in Math. vol. 240 (Springer- Verlag, 1971).Google Scholar
9. Read, R. C., The use of S-functions in combinatorial analysis, Can. J. Math. 20 (1968), 808–841.Google Scholar
10. Knutson, D., Lecture notes on \-rings and the theory of the symmetric group, Lecture notes in Math. vol. 308 (Springer-Verlag, 1973)Google Scholar