Representations of little $q$-Schur algebras
Representations of little $q$-Schur algebras
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DOI：
10.2140/pjm.2012.257.343
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发表时间：
2011-06
期刊：
影响因子：
--
通讯作者：
J. Du;Qiang Fu;Jian-pan Wang
中科院分区：
文献类型：
--
作者：
J. Du;Qiang Fu;Jian-pan Wang
在{DFW}和{Fu 07}中，引入了小q$-Schur代数作为无穷小量子群的同态象.在本文中，我们将研究这些代数的表示。我们将分类小$q$-Schur代数的单模和分类半单模小$q$-Schur代数。此外，通过对n=2的小q-Schur代数的块的分类，确定了单位根为奇数的情况下的有限表示型小q-Schur代数.
In \cite{DFW} and \cite{Fu07}, little $q$-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups. In this paper, we will investigate representations of these algebras. We will classify simple modules for little $q$-Schur algebras and classify semisimple little $q$-Schur algebras. Moreover, through the classification of the blocks of little $q$-Schur algebras for $n=2$, we will determine little $q$-Schur algebras of finite representation type in the odd roots of unity case.