Some representation theory for the modular general linear groups
Some representation theory for the modular general linear groups
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模一般线性群的一些表示理论
DOI：
10.1016/0021-8693(77)90339-8
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发表时间：
1977
影响因子：
0.9
通讯作者：
J. Sullivan
中科院分区：
文献类型：
--
作者：
J. Sullivan
本文给出了一般线性群的某些非零特征的非单表示的结构的一些直接计算。具体地说，我们研究了（1）Z/$2上一般线性群概型G12的Hopf代数O（GZ，）的余代数分支，（2）一对不可约GI，mz-模的扩张群为零的一个充分条件，（3）由不可约GI得到的一类GI，，zlgz-模的合成因子，o-模通过Z-形式的约化模p（cf. [4]）。主要结果是4.5、4.6、5.4和5.5节的命题和推论。
In this paper, we give some direct computations concerning the structure of certain nonsimple representations of the general linear group in nonzero characteristic. Specifically, we study (1) the coalgebra components of the Hopf algebra O (GZ,,,,,) of the general linear group scheme G12 over Z/$2,(2) a sufficient condition for the vanishing of the group of extensions of a pair of irreducible GI, mz-modules,(3) the composition factors of a certain class of Gl,, zlgz modules obtained from irreducible Gl, o-modules by reduction module p of Z-forms (cf.[4]). The main results are the propositions and corollaries of Sections 4.5, 4.6, 5.4, and 5.5.