A characteristic-free approach to the representation theory of Gn☆
A characteristic-free approach to the representation theory of Gn☆
复制标题
Gn☆表示论的无特征方法
DOI：
10.1016/0021-8693(77)90380-5
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发表时间：
1977
影响因子：
0.9
通讯作者：
G. James
中科院分区：
文献类型：
--
作者：
G. James
本文的初衷是寻找 Specht 模块 So 的便捷表征。我们希望描述独立于 S” 的基和场特征。原因是希望有一个简单的测试来确定特定向量是否属于 SA。例如，最好知道 S' 是否包含不动点。本文的最后一节给出了发生这种情况的充分必要条件。假设 X 是 II 的划分。那么 Specht 模块 SA 是 6 的排列模块 MA 的子模块，我们将 SA 描述为 MA 上定义的某些模同态的核的交集。同态是经过精心选择的，以便 [4] 中开发的许多用于处理 n 的两部分划分的技术可以在更广泛的背景下应用。
The origin of this paper was a search for a convenient characterization of the Specht module, So. We wanted the description to be independent of a basis of S” and of the field characteristic. The reason is that it is desirable to have an easy test to decide whether or not a particular vector belongs to SA. For instance, it would be nice to know whether or not S’contains a fixed point. A necessary and sufficient condition for this to happen is given in the final section of this article.Suppose that X is a partition of II. Then the Specht module SA is a submodule of the permutation module MA of 6, on a Young subgroup. We characterize SA as the intersection of the kernels of certain module homomorphisms defined on MA. The homomorphisms are carefully chosen so that many of the techniques developed in [4] for dealing with two-part partitions of n can be applied in a wider context. Theorem 2.4 of [4] is g eneralized here to our Main Theorem (Theorem 9.3).