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Representation-theoretic interpretation of a formula of D. E. Littlewood

Published online by Cambridge University Press:  24 October 2008

Tadeusz Józefiak  and
Jerzy Weyman
Tadeusz Józefiak
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87-100 Toruń, Poland
Jerzy Weyman
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87-100 Toruń, Poland
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Extract

This note is a continuation of our attempts (see [3]) to give a satisfactory representation-theoretic justification of the following formula of D. E. Littlewood:

where sI is the Schur symmetric function corresponding to a partition I, |I| is the weight of I, r(I) is the rank of I, and the summation ranges over all self-conjugate partitions (i.e. partitions I such that I = I where I is the partition conjugate to I).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 193 - 196
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Cartan, H. and Eilenberg, S.. Homological Algebra (Princeton University Press, 1956).Google Scholar
[2]Józefiak, T., Pragacz, P. and Weyman, J.. Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrices. Astérisque 87–88 (1981), 109–189.Google Scholar
[3]Józefiak, T. and Weyman, J.. Symmetric functions and Koszul complexes. Adv. in Math. 56 (1985), 1–8.Google Scholar