Algebraic construction of contragradient quasi-Verma modules in positive characteristic
Algebraic construction of contragradient quasi-Verma modules in positive characteristic
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正特性对梯度拟Verma模的代数构造
DOI：
10.2969/aspm/04010027
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
S. Arkhipov
中科院分区：
文献类型：
--
作者：
S. Arkhipov
本文研究了半单代数群的超代数上一类新的具有正特征的无限维模--拟Verma模。我们提供了一个纯粹的代数结构的整体Grothendieck-Cousin复杂的标准线bundle ${\mathcal L}（\lambda）$上的旗簇的Schubert细胞分层的代数群。我们证明了复杂的直和组成的拟Verma模块的最高权重的形式$w\cdot\lambda$的各种元素$w$的Weyl群。
In the present paper we investigate a new class of infinite-dimensional modules over the hyperalgebra of a semi-simple algebraic group in positive chararacteristic called quasi-Verma modules. We provide a purely algebraic construction of the global Grothendieck-Cousin complex corresponding to the standard line bumdle ${\mathcal L}(\lambda)$ on the Flag variety of the algebraic group stratified by Schubert cells. We prove that the complex consists of direct sums of quasi-Verma modules for the highest weights of the form $w\cdot\lambda$ for various elements $w$ of the Weyl group.