A THEOREM ON THE PLETHYSM OF S-FUNCTIONS
A THEOREM ON THE PLETHYSM OF S-FUNCTIONS
复制标题
S函数体积的定理
DOI：
10.1093/qmath/2.1.161
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发表时间：
1951
影响因子：
0.7
通讯作者：
M. J. Newell
中科院分区：
文献类型：
--
作者：
M. J. Newell
1. Littlewood（1）定义的^-函数的体积在不变量理论中非常有用，其应用的重要性已经由其创始人（2，3等）证明。然而，{A}®{n}的实际计算是相当繁琐的过程。本文证明了一个定理，它是Littlewood所用定理的推广，并表明它大大简化了{A}®{^}的计算。为了说明应用程序的一些结果（不给Littlewood）的伴随五次在任何数量的变量，以及一些plethysms有关的交替伴随类型的一组三次和四次。
1. THE plethysra of^-functions as defined by Littlewood (1) is extremely useful in invariant theory, and the importance of its applications has been demonstrated by its originator (2, 3, etc.). The actual calculation of {A}®{n} is, however, a rather tedious process. This paper contains the proof of a theorem which is a generalization of one used by Littlewood, and it is shown that it simplifies very much the calculation of {A}®{^}. To illustrate the applications some results (not given by Littlewood) on the concomitants of the quintic in any number of variables are given, as well as some plethysms relating to the alternating concomitant types of a set of cubics and quartics.