Symmetric and Exterior Powers, Linear Source Modules and Representations of Schur Superalgebras
Symmetric and Exterior Powers, Linear Source Modules and Representations of Schur Superalgebras
复制标题
DOI：
10.1112/plms/83.3.647
复制
发表时间：
2001-11
影响因子：
1.8
通讯作者：
S. Donkin
中科院分区：
文献类型：
--
作者：
S. Donkin
我们研究一般线性群的模（在任意特征的无限域上），它们是自然模的外幂和对称幂的张量积的直接和。这些模块，我们称之为列表模块，包括 Schur 代数的倾斜模块和单射模块。一方面通过它们与对称群的线性源模的关系来研究这些模，另一方面通过与 Schur 超代数的简单模的关系来研究这些模。列表模块由某些分区对进行参数化。它们用于通过生成器和关系来描述由对称幂和外幂生成的多项式函子的格洛腾迪克环。我们还（J. Grabmeier 的持续工作）描述了对称群的线性源模块的顶点和源。 2000年数学科目分类：20G05、20C30。
We study modules for the general linear group (over an infinite field of arbitrary characteristic) which are direct summands of tensor products of exterior powers and symmetric powers of the natural module. These modules, which we call listing modules, include the tilting modules and the injective modules for Schur algebras. The modules are studied via their relationship to linear source modules for symmetric groups on the one hand, and simple modules for Schur superalgebras on the other. Listing modules are parametrized by certain pairs of partitions. They are used to describe, by generators and relations, the Grothendieck ring of polynomial functors generated by the symmetric and exterior powers. We also (continuing work of J. Grabmeier) describe the vertices and sources of linear source modules for symmetric groups. 2000 Mathematical Subject Classification: 20G05, 20C30.