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Submodules of Specht modules for Weyl groups

Published online by Cambridge University Press:  20 January 2009

Saіt Halicioğlu
Affiliation:
Department of Mathematics Ankara University 06100 Tandoğan Ankara, Turkey
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Abstract

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The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G. D. James. Halicioğlu and Morris describe a possible extension of James' work for Weyl groups in general, where Young tableux are interpreted in terms of root systems. In this paper we show how to construct submodules of Specht modules for Weyl groups.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Al-Aamily, E., Morris, A. O. and Peel, M. H. The representations of the Weyl groups of type Bn, J. Algebra 68 (1981), 298305.CrossRefGoogle Scholar
2. Carter, R. W., Conjugacy classes in the Weyl group, Compositio. Math. 25 (1972), 159.Google Scholar
3. Halicioğlu, S., Specht modules for finite reflection groups, Glasgow Math. J. 37 (1995), 279287.CrossRefGoogle Scholar
4. Halicioğlu, S., A basis of Specht modules for Weyl groups, Turkish J. Math. 18 (1994), 311326.Google Scholar
5. Halicioğlu, S. and Morris, A. O., Specht modules for Weyl groups, Contrib. Alg. Geom. 34 (1993), 257276.Google Scholar
6. James, G. D., The irreducible representations of the symmetric group, Bull. London Math. Soc. 8 (1976), 229232.CrossRefGoogle Scholar
7. Morris, A. O., Representations of Weyl groups over an arbitrary field, Astérisque 87–88 (1981), 267287.Google Scholar
8. Specht, W., Die irreduziblen Darstellungen der symmetrischen Gruppen, Math. Z. 39 (1935), 679711.CrossRefGoogle Scholar