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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, h λ, in terms of Schur functions;

where the operation Srs is defined as follows:

Y 1: 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 λ 1 = λ 2 in the case of S 13 S 23.“

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 S 12 3 S 23 does not appear in the above yet it is not specifically excluded by the rule Y 1.

Information

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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