On the Plethysm of S-Functions

Plunkett, S. P. O.

Canadian journal of mathematics, Tome 24 (1972) no. 3, pp. 541-552

Résumé

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.

Détail

DOI : 10.4153/CJM-1972-047-7

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