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On the Plethysm of S-Functions

Published online by Cambridge University Press:  20 November 2018

S. P. O. Plunkett
S. P. O. Plunkett*
Affiliation:
The University of Southampton, Southampton, England
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Many authors have studied the theory and calculation of the plethysms of S-functions. The significance of S-functions lies in their relationship [9] to the characters of the continuous groups, and plethysms play a crucial role in the determination of branching rules associated with the decomposition of a continuous group into its subgroups [2 ; 14 ; 16]. Tables have been published for the plethysm {λ{ ⊗ {μ{, where (λ) and (μ) are any partitions of l and m, respectively, with Im ≦ 18. These tables have been drawn up both with [1] and without [5] the aid of computers and some results are also known for Im > 18 [3; 4; 7].

The method given here deals with the notion of q-quotients and is based on a theorem of Littlewood's relating these to plethysms of S-functions with symmetric power sums.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 3 , June 1972 , pp. 541 - 552
Copyright
Copyright © Canadian Mathematical Society 1972

References

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