Loewy series of parabolically induced G_1T-Verma modules
Loewy series of parabolically induced G_1T-Verma modules
复制标题
Loewy 系列抛物线诱导 G_1T-Verma 模块
DOI：
10.1017/s1474748014000012
复制
发表时间：
2015
影响因子：
0.9
通讯作者：
Masaharu Kaneda
中科院分区：
文献类型：
--
作者：
Noriyuki Abe;Masaharu Kaneda
我们证明了正特征-梯度代数闭域上约化代数群的Frobenius核的模。特别地，我们得到了由-正则最高权的单模导出的模是刚性的，并确定了它们的Loewy级数，假设了约化代数群的不可约性质的Lusztig猜想，该猜想现在是一个大定理。我们说一个模是刚性的，当且仅当它允许每个子商具有最小长度的唯一过滤，在这种情况下，这种过滤称为Loewy级数。
We show that the modules for the Frobenius kernel of a reductive algebraic group over an algebraically closed field of positive characteristic -graded. In particular, we obtain that the modules induced from the simple modules of -regular highest weights are rigid and determine their Loewy series, assuming the Lusztig conjecture on the irreducible characters for the reductive algebraic groups, which is now a theorem for large . We say that a module is rigid if and only if it admits a unique filtration of minimal length with each subquotient semisimple, in which case the filtration is called the Loewy series.