论文标题
通用Verma模块的Jantzen系数和自由基过滤
Jantzen coefficients and radical filtrations for generalized Verma modules
论文作者
论文摘要
在本文中，我们给出了一个总和公式，用于在抛物线BGG类别的任何（可能是单数）块中概括的Verma模块的根本过滤，可以将其视为通常BGG类别中Verma模块的Jantzen Sum公式的概括。结合Jantzen系数，我们确定所有基本广义Verma模块的自由基过滤。证明利用了抛物线BGG类别的分级版本。还给出了抛物线抛物线BGG类别（可能是单数）积分块中广义VERMA模块的分级分解数和反向分级分解数的显式公式。
In this paper we give a sum formula for the radical filtration of generalized Verma modules in any (possibly singular) blocks of parabolic BGG category which can be viewed as a generalization of Jantzen sum formula for Verma modules in the usual BGG category $\mathcal{O}$. Combined with Jantzen coefficients, we determine the radical filtrations for all basic generalized Verma modules. The proof makes use of the graded version of parabolic BGG category. Explicit formulae for the graded decomposition numbers and inverse graded decomposition numbers of generalized Verma modules in any (possibly singular) integral blocks of the parabolic BGG category are also given.
