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A note on lemmas of Green and Kondo

Published online by Cambridge University Press:  24 October 2008

A. O. Morris
A. O. Morris
Affiliation:
University College of Wales, Aberystwyth
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Extract

Let R be the field of rational numbers, {x} = {x1, z2, …}, {y} = {y1, y2, …} be two countably infinite sets of variables and t an indeterminate. Let (λ) = (λ1, λ2, …, λm) be a partition of n. Then Littlewood (5) has shown that

can be expressed in the form

where Qλ(x, t) and Qλ(y, t) denote certain symmetric functions on the sets {x} and {y} respectively. In addition

where is the partition of n conjugate to (λ). In fact, Littlewood (5) showed that

where the summation is over all terms obtained by permutations of the variables xi (i = 1, 2, …) and

.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 83 - 85
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Green, J. A.The characters of the finite general linear groups. Trans. Am. Math. Soc. 80 (1955), 402–47.CrossRefGoogle Scholar
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