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Modular spin representations of the symmetric group

Published online by Cambridge University Press:  24 October 2008

R. H. Jones
R. H. Jones
Affiliation:
Department of Pure Mathematics, University College of Wales, Aberystwyth Department of Mathematics, Lanchester Polytechnic, Coventry
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Extract

1. Let Γn be the representation group or spin group (4, 9) of Sn. Then the irreducible representations of Γn are of two distinct types. These are (a) ordinary representations, which are the irreducible representations of the symmetric group and (b) spin or projective representations. Corresponding to every partition (λ) = (λ1, λ2, …, λm) of n with λ1 > λ2 > … > λm > 0 there is an irreducible spin representation 〈λ〉 of Γn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 365 - 372
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Brauer, R. and Robinson, G. de B.On a conjecture by Nakayama. Trans. Royal Soc. Canada Sec. III (3) 41 (1947), 11–25.Google Scholar
(2)Frame, J. S., Robinson, G. de B. and Thrall, R. M.The hook graphs of the symmetric group. Canad. J. Math. 6 (1954), 316–324.CrossRefGoogle Scholar
(3)Littlewood, D. E.The theory of group characters and matrix representations of groups (second edition) (Oxford, 1950).Google Scholar
(4)Morris, A. O.The spin representation of the symmetric group. Proc. London Math. Soc. (3) 12 (1962), 55–76.CrossRefGoogle Scholar
(5)Morris, A. O.The spin representation of the symmetric group. Canad. J. Math. 17 (1965), 543–549.CrossRefGoogle Scholar
(6)Nakayama, T.On some modular properties of irreducible representations of the symmetric group, 1, 11. J. Math. Soc. Japan 17 (1941), 165–184, 277–294.CrossRefGoogle Scholar
(7)Robinson, G. de B.On the representation of the symmetric group 111. Amer. J. Math. 70 (1948), 277–294.CrossRefGoogle Scholar
(8)Robinson, G. de B.Representation theory of the symmetric group (Toronto, 1961).Google Scholar
(9)Scrur, I.Über die Darstellung der symmetrischen und der alternierenden Oruppe duroh gebrochene lineare substitionen. J. Reine Angew. Math. 139 (1911), 155–250.Google Scholar