Tensor induction of generalized characters and permutation characters
Tensor induction of generalized characters and permutation characters
复制标题
广义特征和排列特征的张量归纳
DOI：
10.1215/ijm/1256046375
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发表时间：
1983
影响因子：
0.6
通讯作者：
I. Isaacs
中科院分区：
文献类型：
--
作者：
D. Gluck;I. Isaacs
设H是有限群G的子群，F是任意域.有一个称为“张量归纳法”的过程，可以将其应用于任意FH-模W，以获得维数等于（dim W）IG：nl的FG-模W。粗略地说，W是W的IG 'H副本的张量积，G的作用置换因子的方式与置换构成普通诱导模Wa的直和项的方式大致相同。张量诱导模的构造是由Dade（[2]的第9节）和Dress独立地介绍的。张量归纳法已被Dade，T. R.伯杰河，巴西-地kn 6 rr和其他人研究了表示论中的某些问题。张量归纳法的论述，包括构造的细节，可以在[1]和[5]中找到。现在让我们把注意力限制在F C的情况下，复数。如果W提供字符0 char（H），则不难计算W（R）提供的字符，我们用0（R）表示。这样得到的公式用0的值表示0的值，并且这个公式可以用来定义H的任何类函数的（R）。结果是G的一个类函数，当然，一般来说，它不是一个特征标。
Let H be a subgroup of a finite group G and let F be any field. There is a procedure called "tensor induction" which one can apply to an arbitrary FH-module W to obtain an FG-module W of dimension equal to (dim W)IG:nl. Roughly speaking, W is the tensor product of IG’H copies of W, and the action of G permutes the factors in much the same way that it permutes the direct summands which make up the ordinary induced module Wa. The construction of the tensor-induced module was introduced by Dade (Section 9 of [2]) and independently by Dress [3]. Tensor induction has been used by Dade, T. R. Berger, R. Kn6rr and others to study certain problems in representation theory. Expositions of tensor induction, including the details of the construction, can be found in [1] and [5]. Let us now limit attention to the case where F C, the complex numbers. If W affords the character 0 char(H), it is not hard to compute the character afforded by W(R), which we denote by 0(R). The formula thus obtained expresses the values of 0 in terms of the values of 0, and this formula can be used to define (R) for any class function of H. What results is a class function of G which is not, of course, in general, a character.