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A Note on Young's Raising Operator

Published online by Cambridge University Press:  20 November 2018

Glânffrwd P. Thomas
Glânffrwd P. Thomas*
Affiliation:
Open University Production Centre, Milton Keynes, Great Britain
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Consider the following formula due to Young [7] for the calculation of the homogeneous product sum, hλ, in terms of Schur functions;

where the operation Srs is defined as follows:

Y1: Srs, where r < s, “represents the operation of moving one letter from the s-th row up to the r-th row; and the resulting term is regarded as zero, when any row becomes less than a row below it, or when letters from the same row overlap; as, for instance, happens when λ1 = λ2 in the case of S13S23.“

The following example of the above is given by Robinson [4].

Calculation by other means shows that the above analysis of h(3,2,1) is correct; however, it will be noticed that the operator S123S23 does not appear in the above yet it is not specifically excluded by the rule Y1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 1 , 01 February 1981 , pp. 49 - 54
Copyright
Copyright © Canadian Mathematical Society 1981

References

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