Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-15T10:54:38.516Z Has data issue: false hasContentIssue false

Frobenius Symbols and the Groups SsGL(n), O(n) and Sp(n)

Published online by Cambridge University Press:  20 November 2018

Y. J. Abramsky
Affiliation:
The University of Southampton, Southampton, England; University of Toronto, Toronto, Ontario
H. A. Jahn
Affiliation:
The University of Southampton, Southampton, England; University of Toronto, Toronto, Ontario
R. C. King
Affiliation:
The University of Southampton, Southampton, England; University of Toronto, Toronto, Ontario
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.

Frobenius [2; 3] introduced the symbols

to specify partitions and the corresponding irreducible representations of the symmetric group Ss.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Frame, J. S., Robinson, G. de B., and Thrall, R. M., The hook graphs of the symmetric group, Can. J. Math. 6 (1954), 316324.Google Scholar
2. Frobenius, F. G., Über die Charaktere der symmetrischen Gruppe, Sitz. Ber. Preuss. Akad., Berlin (1900), 516534.Google Scholar
3. Frobenius, F. G., Über die charakteristischen Einheiten der symmetrischen Gruppe, Sitz. Ber. Preuss. Akad., Berlin (1903), 328358.Google Scholar
4. Hamermesh, M., Group theory and its application to physical problems (Addison-Wesley, Reading, Massachusetts, 1962).Google Scholar
5. King, R. C., The dimensions of irreducible tensor representations of the orthogonal and symplectic groups, Can. J. Math. 23 (1971), 176188.Google Scholar
6. King, R. C., Modification rules and products of irreducible representations of the unitary, orthogonal and symplectic groups, J. Math. Phys. 12 (1971), 15881598.Google Scholar
7. Littlewood, D. E., The theory of group characters, 2nd Edition (University Press, Oxford, 1950).Google Scholar
8. Littlewood, D. E., Products and plethysms of characters with orthogonal, symplectic and symmetric groups, Can. J. Math. 10 (1958), 1732.Google Scholar
9. Newell, M. J., Modification rules for the orthogonal and symplectic groups, Proc. Roy. Irish. Acad. Sect A 54 (1951), 153163.Google Scholar
10. Robinson, G. de B., Representation theory of the symmetric group (The University Press, Edinburgh, 1961).Google Scholar