论抛物线维尔马模块的根滤波

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2024-05-14 DOI:10.4310/mrl.2023.v30.n5.a7

Jun Hu, Wei Xiao

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引用次数: 0

摘要

在本文中，我们给出了抛物面 BGG 类中任何（可能是奇异的）块中的抛物面 Verma 模块的基滤波总和公式。它可以看作是通常 BGG 范畴 $\mathcal{O}$ 中 Verma 模块的 Jantzen 求和公式的广义化。证明利用了抛物线 BGG 范畴的分级版本。还给出了在抛物 BGG 范畴的任何（可能是奇异的）积分块中抛物 Verma 模块的分级分解数和反分级分解数的明确公式，这些公式都是用卡兹丹-卢兹蒂格多项式表示的。

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On radical filtrations of parabolic Verma modules

In this paper we give a sum formula for the radical filtration of parabolic Verma modules in any (possibly singular) blocks of parabolic BGG category. It can be viewed as a generalization of the Jantzen sum formula for Verma modules in the usual BGG category $\mathcal{O}$. 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 parabolic Verma modules in any (possibly singular) integral blocks of the parabolic BGG category are also given in terms of the Kazhdan–Lusztig polynomials.

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来源期刊

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.