On the Plethysm of S-Functions
On the Plethysm of S-Functions
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关于 S 函数的丰富性
DOI：
10.4153/cjm-1972-047-7
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发表时间：
1972
期刊：
影响因子：
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通讯作者：
S. P. O. Plunkett
中科院分区：
文献类型：
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作者：
S. P. O. Plunkett
许多作者研究了S函数的多解性的理论和计算。S函数的意义在于它们与连续群的性质的关系[9]，而多体在确定一个连续群分解成它的子群时的分支规则[2；14；16]中起着至关重要的作用。λ{⊗{μ{，其中(λ)和(μ)分别是L和m的任意划分，其中Im≦18。这些表是用[1]和不用[5]计算机绘制的，有些结果对Im>；18[3；4；7]也是已知的。本文给出的方法涉及q-商的概念，并基于Littlewood的一个定理，该定理将q-商与具有对称幂和的S函数的多重性联系起来。
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.