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Some combinatorial results involving shifted Young diagrams

Published online by Cambridge University Press:  24 October 2008

A. O. Morris  and
A. K. Yaseen
A. O. Morris
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth, Dyfed SY23 3BZ
A. K. Yaseen
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth, Dyfed SY23 3BZ
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Extract

In [6] the first author introduced some combinatorial concepts involving Young diagrams corresponding to partitions with distinct parts and applied them to the projective representations of the symmetric group Sn. A conjecture concerning the p-block structure of the projective representations of Sn was formulated in terms of these concepts which corresponds to the well-known, but long proved, Nakayama ‘conjecture’ for the p-block structure of the linear representations of Sn. This conjecture has recently been proved by Humphreys [1].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 23 - 31
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Humphreys, J. F.. Blocks of projective representations of the symmetric groups. (To appear.)Google Scholar
[2]James, G. D.. Some combinatorial results involving Young diagrams. Math. Proc. Cambridge Philos. Soc. 83 (1978), 1–10.CrossRefGoogle Scholar
[3]James, G. D. and Kerber, A.. The Representation Theory of the Symmetric Group (Addison-Wesley, 1981).Google Scholar
[4]Jones, R. H.. Modular spin representations of the symmetric group. Proc. Cambridge Philos. Soc. 69 (1971), 365–371.CrossRefGoogle Scholar
[5]Macdonald, I. G.. Symmetric Functions and Hall Polynomials (Clarendon Press, 1979).Google Scholar
[6]Morris, A. O.. The spin representations of the symmetric group. Canad. J. Math. 17 (1965), 543–549.CrossRefGoogle Scholar