低阶截断多项式环的模不变量

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-07-04 DOI:10.1016/j.jalgebra.2025.06.034

Le Minh Ha , Nguyen Dang Ho Hai , Nguyen Van Nghia

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引用次数: 0

摘要

我们验证了Lewis， Reiner和Stanton关于截断多项式环的不变量环的Hilbert级数的猜想，这些猜想适用于所有3阶以下的抛物子群。这是通过为所讨论的每个不变环构造一组显式生成器来实现的。我们还提出了关于Steenrod代数和Dickson代数在一般线性群作用下对不变环的某自然滤过作用的一个猜想。

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On modular invariants of the truncated polynomial rings in low ranks

We verify the conjectures due to Lewis, Reiner, and Stanton about the Hilbert series of the invariant ring of the truncated polynomial ring for all parabolic subgroups up to rank 3. This is done by constructing an explicit set of generators for each invariant ring in question. We also propose a conjecture concerning the action of the Steenrod algebra and the Dickson algebra on a certain naturally occurring filtration of the invariant ring under the action of the general linear group.

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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.