Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-07-06T17:28:30.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Induced Representations and Alternating Groups

Published online by Cambridge University Press:  20 November 2018

B. M. Puttaswamaiah  and
G. de B. ROBINSON
B. M. Puttaswamaiah
Affiliation:
Carleton University and University of Toronto
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.

This paper is based on part of the thesis of one of the authors (5), submitted at the University of Toronto in 1963. In the first part of the paper a result on induced representations (2, 4, 9) is generalized slightly and a number of corollaries are derived. In the rest of the paper a special case of this result is applied to put the representation theory of the alternating group on a par with that of the symmetric group. A knowledge of the representation theory of Sn (7) on the part of the reader is assumed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 587 - 601
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Frobenius, G., Über die Charaktere der alternier enden Gruppe, S. B. Preuss. Akad. Wiss. (1901), 303-315.Google Scholar
2. Littlewood, D. E., Kronecker product of symmetric group representations, J. London Math. Soc, 81 (1956), 89–93.Google Scholar
3. Mackey, G. W., On the induced representations of groups, Am. J. Math., 73 (1951), 576–592.Google Scholar
4. Osima, M., Some notes on the induced representations of a group, Jap. J. Math., 21 (1951), 191–196.Google Scholar
5. Puttaswamaiah, B. M., Thesis: Group representations, University of Toronto (1963).Google Scholar
6. Puttaswamaiah, B. M., On the reduction of the permutation representation, Can. Math. Bull., 6 (1963), 385–395.Google Scholar
7. de, G. Robinson, B., Representation theory of the symmetric group (Toronto, 1962).Google Scholar
8. de, G. B. Robinson, Modular representations of Sn , Can. J. Math., 16 (1964), 191–203.Google Scholar
9. de, G. B. Robinson and Taulbee, O. E., The reduction of the inner product of two representations ofSn, Proc. Natl. Acad. Sci., 40 (1954), 723–726.Google Scholar
10. Thrall, R. M., Young's semi-normal representations of Sn, Duke Math. J., 8 (1941), 611–624.Google Scholar