Ariki-Koike代数的移动向量和核心块

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2026-05-15 Epub Date: 2026-01-29 DOI:10.1016/j.jalgebra.2026.01.028

Yanbo Li , Xiangyu Qi , Kai Meng Tan

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引用次数: 0

摘要

我们通过移动向量对Ariki-Koike代数的核心块进行分类。利用这一分类，我们得到了两个核心块之间作用域等价的充分必要条件，并将一个核心块中的简单模块数表示为经典Kostka数。在多电荷移动矢量的一定条件下，我们进一步将这些块在特征零点处的梯度分解数与A型Iwahori-Hecke代数的梯度分解数联系起来。

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Moving vectors and core blocks of Ariki-Koike algebras

We classify the core blocks of Ariki-Koike algebras by their moving vectors. Using this classification, we obtain a necessary and sufficient condition for Scopes equivalence between two core blocks, and express the number of simple modules lying in a core block as a classical Kostka number. Under certain conditions on the multicharge and moving vector, we further relate the graded decomposition numbers of these blocks in characteristic zero to the graded decomposition numbers of the Iwahori-Hecke algebras of type A.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.